From 6903f4ddb7592d5c0250a071e8f0ab6e927b5793 Mon Sep 17 00:00:00 2001 From: Marek Kaluba Date: Fri, 5 Jul 2024 19:16:08 +0200 Subject: [PATCH] reorganize small perm groups --- test/dixon.jl | 3 +- test/runtests.jl | 27 + test/smallgroups.jl | 1946 +++++++++++++++++++++++++++++++++++-------- 3 files changed, 1627 insertions(+), 349 deletions(-) diff --git a/test/dixon.jl b/test/dixon.jl index 90e5cdf..b36211e 100644 --- a/test/dixon.jl +++ b/test/dixon.jl @@ -226,7 +226,8 @@ end end @time @testset "SmallPermGroups" begin - for (ord, groups) in SmallPermGroups + for ord in 2:30 + groups = SmallPermGroups[ord] @testset "SmallGroup($ord, $n)" for (n, G) in enumerate(groups) @test Characters.irreducible_characters(G) isa Vector{<:Characters.Character} diff --git a/test/runtests.jl b/test/runtests.jl index 0e3005c..9f5c67e 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -47,3 +47,30 @@ if VERSION >= v"1.7.0" && !haskey(ENV, "CI") end end +# Small groups generation: +#= GAP code: +H := []; +for i in [1..63] do + Add(H, List(AllSmallGroups(i), G->Image(IsomorphismPermGroup(G)))); +od; +PrintTo("/tmp/groups.gap", H); +=# + +#=julia code +GAPgroups_str = join(readlines("/tmp/groups.gap"), ""); +GAPgroups_str = replace(GAPgroups_str, "Group"=>"\nPermGroup"); +GAPgroups_str = replace(GAPgroups_str, r" *"=>""); +perm_regex = r"((\(\d+(,\d+)*\)?)+)"; +let fn = joinpath(@__DIR__, "smallgroups.jl") + open(fn, "w") do file + + print(file, """ + import PermutationGroups: PermGroup, @perm_str + + const SmallPermGroups = """) + println(file, replace(GAPgroups_str, perm_regex=> s"perm\"\1\"")) + end + read(fn, String) +end +=# + diff --git a/test/smallgroups.jl b/test/smallgroups.jl index c7165fe..ace6d1c 100644 --- a/test/smallgroups.jl +++ b/test/smallgroups.jl @@ -1,350 +1,1600 @@ -#= GAP code: -H := []; -for i in [2..30] do - Add(H, List(AllSmallGroups(i), G->Image(IsomorphismPermGroup(G)))); -od; -PrintTo("/tmp/groups.gap", H); -=# - -#=julia code -GAPgroups_str = join(readlines("/tmp/group.gap"), ""); -GAPgroups_str = replace(GAPgroups_str, "Group"=>"\nPermGroup"); -GAPgroups_str = replace(GAPgroups_str, r" *"=>""); -perm_regex = r"((\(\d+(,\d+)*\)?)+)"; -print(Meta.parse(replace(GAPgroups_str, perm_regex=> s"perm\"\1\""))) -=# - import PermutationGroups: PermGroup, @perm_str -const SmallPermGroups = Dict( - i + 1 => x for (i, x) in enumerate([ - [PermGroup([perm"(1,2)"])], - [PermGroup([perm"(1,2,3)"])], - [PermGroup([perm"(1,2,3,4)"]), PermGroup([perm"(1,2)", perm"(3,4)"])], - [PermGroup([perm"(1,2,3,4,5)"])], - [ - PermGroup([perm"(1,2)(3,6)(4,5)", perm"(1,3,5)(2,4,6)"]), - PermGroup([perm"(1,2)", perm"(3,4,5)"]), - ], - [PermGroup([perm"(1,2,3,4,5,6,7)"])], - [ - PermGroup([perm"(1,2,3,4,5,6,7,8)"]), - PermGroup([perm"(1,2)", perm"(3,4,5,6)"]), - PermGroup([ - perm"(1,2)(3,8)(4,6)(5,7)", - perm"(1,3)(2,5)(4,7)(6,8)", - perm"(1,4)(2,6)(3,7)(5,8)", - ]), - PermGroup([ - perm"(1,2,4,6)(3,8,7,5)", - perm"(1,3,4,7)(2,5,6,8)", - perm"(1,4)(2,6)(3,7)(5,8)", - ]), - PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)"]), - ], - [ - PermGroup([perm"(1,2,3,4,5,6,7,8,9)"]), - PermGroup([perm"(1,2,3)", perm"(4,5,6)"]), - ], - [ - PermGroup([ - perm"(1,2)(3,10)(4,9)(5,8)(6,7)", - perm"(1,3,5,7,9)(2,4,6,8,10)", - ]), - PermGroup([perm"(1,2)", perm"(3,4,5,6,7)"]), - ], - [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11)"])], - [ - PermGroup([ - perm"(1,2,3,5)(4,10,7,12)(6,11,9,8)", - perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,12)", - perm"(1,4,8)(2,6,10)(3,7,11)(5,9,12)", - ]), - PermGroup([perm"(1,2,3)", perm"(4,5,6,7)"]), - PermGroup([ - perm"(1,2,5)(3,7,12)(4,11,9)(6,10,8)", - perm"(1,3)(2,6)(4,8)(5,9)(7,11)(10,12)", - perm"(1,4)(2,7)(3,8)(5,10)(6,11)(9,12)", - ]), - PermGroup([ - perm"(1,2)(3,5)(4,10)(6,8)(7,12)(9,11)", - perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,12)", - perm"(1,4,8)(2,6,10)(3,7,11)(5,9,12)", - ]), - PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7)"]), - ], - [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13)"])], - [ - PermGroup([ - perm"(1,2)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", - perm"(1,3,5,7,9,11,13)(2,4,6,8,10,12,14)", - ]), - PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9)"]), - ], - [PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8)"])], - [ - PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)"]), - PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8)"]), - PermGroup([ - perm"(1,2,5,8)(3,12,10,16)(4,7,11,14)(6,15,13,9)", - perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)", - perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)", - perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", - ]), - PermGroup([ - perm"(1,2,5,8)(3,12,10,16)(4,7,11,14)(6,15,13,9)", - perm"(1,3,4,9)(2,6,7,12)(5,10,11,15)(8,13,14,16)", - perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)", - perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", - ]), - PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10)"]), - PermGroup([ - perm"(1,2,4,7,5,8,11,14)(3,13,9,16,10,6,15,12)", - perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)", - perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", - perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", - ]), - PermGroup([ - perm"(1,2)(3,12)(4,14)(5,8)(6,9)(7,11)(10,16)(13,15)", - perm"(1,3)(2,6)(4,15)(5,10)(7,16)(8,13)(9,11)(12,14)", - perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", - perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", - ]), - PermGroup([ - perm"(1,2,5,8)(3,12,10,16)(4,14,11,7)(6,15,13,9)", - perm"(1,3)(2,6)(4,15)(5,10)(7,16)(8,13)(9,11)(12,14)", - perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", - perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", - ]), - PermGroup([ - perm"(1,2,5,8)(3,12,10,16)(4,14,11,7)(6,15,13,9)", - perm"(1,3,5,10)(2,6,8,13)(4,15,11,9)(7,16,14,12)", - perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", - perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", - ]), - PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8)"]), - PermGroup([ - perm"(1,2)(3,13)(4,7)(5,8)(6,10)(9,16)(11,14)(12,15)", - perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)", - perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)", - perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", - ]), - PermGroup([ - perm"(1,2,5,8)(3,13,10,6)(4,7,11,14)(9,16,15,12)", - perm"(1,3,5,10)(2,6,8,13)(4,9,11,15)(7,12,14,16)", - perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)", - perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", - ]), - PermGroup([ - perm"(1,2)(3,13)(4,7)(5,8)(6,10)(9,16)(11,14)(12,15)", - perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)", - perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", - perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", - ]), - PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8)"]), - ], - [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)"])], - [ - PermGroup([ - perm"(1,2)(3,18)(4,12)(5,17)(6,9)(7,16)(8,15)(10,14)(11,13)", - perm"(1,3,7,4,8,13,9,14,17)(2,5,10,6,11,15,12,16,18)", - perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)", - ]), - PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11)"]), - PermGroup([ - perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,16)(11,14)(13,18)(15,17)", - perm"(1,3,7)(2,5,10)(4,8,13)(6,11,15)(9,14,17)(12,16,18)", - perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)", - ]), - PermGroup([ - perm"(1,2)(3,10)(4,12)(5,7)(6,9)(8,18)(11,17)(13,16)(14,15)", - perm"(1,3,7)(2,5,10)(4,8,13)(6,11,15)(9,14,17)(12,16,18)", - perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)", - ]), - PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8)"]), - ], - [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)"])], - [ - PermGroup([ - perm"(1,2,3,5)(4,18,7,20)(6,19,9,16)(8,14,11,17)(10,15,13,12)", - perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,20)", - perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)", - ]), - PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9)"]), - PermGroup([ - perm"(1,2,3,5)(4,10,19,17)(6,11,20,12)(7,13,16,14)(8,18,15,9)", - perm"(1,3)(2,5)(4,19)(6,20)(7,16)(8,15)(9,18)(10,17)(11,12)(13,14)", - perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)", - ]), - PermGroup([ - perm"(1,2)(3,5)(4,18)(6,16)(7,20)(8,14)(9,19)(10,12)(11,17)(13,15)", - perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,20)", - perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)", - ]), - PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9)"]), - ], - [ - PermGroup([ - perm"(1,2,4)(3,8,16)(5,10,12)(6,14,7)(9,20,19)(11,21,15)(13,18,17)", - perm"(1,3,6,9,12,15,18)(2,5,8,11,14,17,20)(4,7,10,13,16,19,21)", - ]), - PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10)"]), - ], - [ - PermGroup([ - perm"(1,2)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", - perm"(1,3,5,7,9,11,13,15,17,19,21)(2,4,6,8,10,12,14,16,18,20,22)", - ]), - PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11,12,13)"]), - ], - [ - PermGroup([ - perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)", - ]), - ], - [ - PermGroup([ - perm"(1,2,3,6,4,7,9,13)(5,16,10,21,11,22,17,24)(8,18,14,19,15,23,20,12)", - perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)", - perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", - perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", - ]), - PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11)"]), - PermGroup([ - perm"(1,2,6)(3,8,20)(4,16,13)(5,9,15)(7,14,10)(11,18,24)(12,23,21)(17,22,19)", - perm"(1,3,5,11)(2,7,9,17)(4,19,12,10)(6,13,15,21)(8,23,18,16)(14,24,22,20)", - perm"(1,4,5,12)(2,8,9,18)(3,10,11,19)(6,14,15,22)(7,16,17,23)(13,20,21,24)", - perm"(1,5)(2,9)(3,11)(4,12)(6,15)(7,17)(8,18)(10,19)(13,21)(14,22)(16,23)(20,24)", - ]), - PermGroup([ - perm"(1,2,4,7)(3,13,9,6)(5,16,11,22)(8,19,15,12)(10,24,17,21)(14,18,20,23)", - perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)", - perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", - perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", - ]), - PermGroup([ - perm"(1,2)(3,6)(4,7)(5,16)(8,12)(9,13)(10,21)(11,22)(14,18)(15,19)(17,24)(20,23)", - perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)", - perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", - perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", - ]), - PermGroup([ - perm"(1,2)(3,13)(4,7)(5,16)(6,9)(8,12)(10,24)(11,22)(14,23)(15,19)(17,21)(18,20)", - perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)", - perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", - perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", - ]), - PermGroup([ - perm"(1,2,4,7)(3,6,9,13)(5,16,11,22)(8,19,15,12)(10,21,17,24)(14,23,20,18)", - perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)", - perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", - perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", - ]), - PermGroup([ - perm"(1,2)(3,13)(4,7)(5,16)(6,9)(8,12)(10,24)(11,22)(14,23)(15,19)(17,21)(18,20)", - perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)", - perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", - perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", - ]), - PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9)"]), - PermGroup([ - perm"(1,2)(3,14)(4,7)(5,8)(6,10)(9,21)(11,15)(12,16)(13,18)(17,24)(19,22)(20,23)", - perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)", - perm"(1,4,11)(2,7,15)(3,9,17)(5,12,19)(6,13,20)(8,16,22)(10,18,23)(14,21,24)", - perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,19)(13,21)(15,22)(17,23)(20,24)", - ]), - PermGroup([ - perm"(1,2,5,8)(3,14,10,6)(4,7,12,16)(9,21,18,13)(11,15,19,22)(17,24,23,20)", - perm"(1,3,5,10)(2,6,8,14)(4,9,12,18)(7,13,16,21)(11,17,19,23)(15,20,22,24)", - perm"(1,4,11)(2,7,15)(3,9,17)(5,12,19)(6,13,20)(8,16,22)(10,18,23)(14,21,24)", - perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,19)(13,21)(15,22)(17,23)(20,24)", - ]), - PermGroup([ - perm"(1,2)(3,13)(4,8)(5,7)(6,9)(10,21)(11,20)(12,16)(14,18)(15,17)(19,24)(22,23)", - perm"(1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16)", - perm"(1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24)", - perm"(1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24)", - ]), - PermGroup([ - perm"(1,2)(3,6)(4,7)(5,8)(9,13)(10,14)(11,15)(12,16)(17,20)(18,21)(19,22)(23,24)", - perm"(1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16)", - perm"(1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24)", - perm"(1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24)", - ]), - PermGroup([ - perm"(1,2)(3,6)(4,7)(5,16)(8,12)(9,13)(10,21)(11,22)(14,18)(15,19)(17,24)(20,23)", - perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)", - perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", - perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", - ]), - PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8,9)"]), - ], - [ - PermGroup([ - perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)", - ]), - PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10)"]), - ], - [ - PermGroup([ - perm"(1,2)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", - perm"(1,3,5,7,9,11,13,15,17,19,21,23,25)(2,4,6,8,10,12,14,16,18,20,22,24,26)", - ]), - PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11,12,13,14,15)"]), - ], - [ - PermGroup([ - perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)", - ]), - PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11,12)"]), - PermGroup([ - perm"(1,2,5)(3,14,25)(4,7,12)(6,19,17)(8,26,24)(9,22,11)(10,15,20)(13,27,16)(18,23,21)", - perm"(1,3,8)(2,6,13)(4,9,16)(5,11,18)(7,14,21)(10,17,23)(12,19,24)(15,22,26)(20,25,27)", - perm"(1,4,10)(2,7,15)(3,9,17)(5,12,20)(6,14,22)(8,16,23)(11,19,25)(13,21,26)(18,24,27)", - ]), - PermGroup([ - perm"(1,2,5,4,7,12,10,15,20)(3,14,25,9,22,11,17,6,19)(8,26,24,16,13,27,23,21,18)", - perm"(1,3,8)(2,6,13)(4,9,16)(5,11,18)(7,14,21)(10,17,23)(12,19,24)(15,22,26)(20,25,27)", - perm"(1,4,10)(2,7,15)(3,9,17)(5,12,20)(6,14,22)(8,16,23)(11,19,25)(13,21,26)(18,24,27)", - ]), - PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9)"]), - ], - [ - PermGroup([ - perm"(1,2,3,5)(4,26,7,28)(6,27,9,24)(8,22,11,25)(10,23,13,20)(12,18,15,21)(14,19,17,16)", - perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,28)", - perm"(1,4,8,12,16,20,24)(2,6,10,14,18,22,26)(3,7,11,15,19,23,27)(5,9,13,17,21,25,28)", - ]), - PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11)"]), - PermGroup([ - perm"(1,2)(3,5)(4,26)(6,24)(7,28)(8,22)(9,27)(10,20)(11,25)(12,18)(13,23)(14,16)(15,21)(17,19)", - perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,28)", - perm"(1,4,8,12,16,20,24)(2,6,10,14,18,22,26)(3,7,11,15,19,23,27)(5,9,13,17,21,25,28)", - ]), - PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9,10,11)"]), - ], - [ - PermGroup([ - perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)", - ]), - ], - [ - PermGroup([ - perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,18)(11,15)(13,16)(14,24)(17,21)(19,22)(20,28)(23,26)(25,30)(27,29)", - perm"(1,3,7,13,19)(2,5,10,16,22)(4,8,14,20,25)(6,11,17,23,27)(9,15,21,26,29)(12,18,24,28,30)", - perm"(1,4,9)(2,6,12)(3,8,15)(5,11,18)(7,14,21)(10,17,24)(13,20,26)(16,23,28)(19,25,29)(22,27,30)", - ]), - PermGroup([ - perm"(1,2)(3,5)(4,24)(6,21)(7,10)(8,28)(9,18)(11,26)(12,15)(13,30)(14,23)(16,29)(17,20)(19,27)(22,25)", - perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,27)(21,26,29)(24,28,30)", - perm"(1,4,9,15,21)(2,6,12,18,24)(3,8,14,20,26)(5,11,17,23,28)(7,13,19,25,29)(10,16,22,27,30)", - ]), - PermGroup([ - perm"(1,2)(3,10)(4,24)(5,7)(6,21)(8,30)(9,18)(11,29)(12,15)(13,28)(14,27)(16,26)(17,25)(19,23)(20,22)", - perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,27)(21,26,29)(24,28,30)", - perm"(1,4,9,15,21)(2,6,12,18,24)(3,8,14,20,26)(5,11,17,23,28)(7,13,19,25,29)(10,16,22,27,30)", - ]), - PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10)"]), - ], - ]) -) +const SmallPermGroups = [ + [PermGroup(perm"()")], + [PermGroup([perm"(1,2)"])], + [PermGroup([perm"(1,2,3)"])], + [PermGroup([perm"(1,2,3,4)"]), PermGroup([perm"(1,2)", perm"(3,4)"])], + [PermGroup([perm"(1,2,3,4,5)"])], + [ + PermGroup([perm"(1,2)(3,6)(4,5)", perm"(1,3,5)(2,4,6)"]), + PermGroup([perm"(1,2)", perm"(3,4,5)"]), + ], + [PermGroup([perm"(1,2,3,4,5,6,7)"])], + [ + PermGroup([perm"(1,2,3,4,5,6,7,8)"]), + PermGroup([perm"(1,2)", perm"(3,4,5,6)"]), + PermGroup([ + perm"(1,2)(3,8)(4,6)(5,7)", + perm"(1,3)(2,5)(4,7)(6,8)", + perm"(1,4)(2,6)(3,7)(5,8)", + ]), + PermGroup([ + perm"(1,2,4,6)(3,8,7,5)", + perm"(1,3,4,7)(2,5,6,8)", + perm"(1,4)(2,6)(3,7)(5,8)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)"]), + ], + [ + PermGroup([perm"(1,2,3,4,5,6,7,8,9)"]), + PermGroup([perm"(1,2,3)", perm"(4,5,6)"]), + ], + [ + PermGroup([ + perm"(1,2)(3,10)(4,9)(5,8)(6,7)", + perm"(1,3,5,7,9)(2,4,6,8,10)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6,7)"]), + ], + [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11)"])], + [ + PermGroup([ + perm"(1,2,3,5)(4,10,7,12)(6,11,9,8)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,12)", + perm"(1,4,8)(2,6,10)(3,7,11)(5,9,12)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6,7)"]), + PermGroup([ + perm"(1,2,5)(3,7,12)(4,11,9)(6,10,8)", + perm"(1,3)(2,6)(4,8)(5,9)(7,11)(10,12)", + perm"(1,4)(2,7)(3,8)(5,10)(6,11)(9,12)", + ]), + PermGroup([ + perm"(1,2)(3,5)(4,10)(6,8)(7,12)(9,11)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,12)", + perm"(1,4,8)(2,6,10)(3,7,11)(5,9,12)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7)"]), + ], + [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13)"])], + [ + PermGroup([ + perm"(1,2)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", + perm"(1,3,5,7,9,11,13)(2,4,6,8,10,12,14)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9)"]), + ], + [PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8)"])], + [ + PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)"]), + PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8)"]), + PermGroup([ + perm"(1,2,5,8)(3,12,10,16)(4,7,11,14)(6,15,13,9)", + perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)", + perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)", + perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", + ]), + PermGroup([ + perm"(1,2,5,8)(3,12,10,16)(4,7,11,14)(6,15,13,9)", + perm"(1,3,4,9)(2,6,7,12)(5,10,11,15)(8,13,14,16)", + perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)", + perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10)"]), + PermGroup([ + perm"(1,2,4,7,5,8,11,14)(3,13,9,16,10,6,15,12)", + perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)", + perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", + perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", + ]), + PermGroup([ + perm"(1,2)(3,12)(4,14)(5,8)(6,9)(7,11)(10,16)(13,15)", + perm"(1,3)(2,6)(4,15)(5,10)(7,16)(8,13)(9,11)(12,14)", + perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", + perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", + ]), + PermGroup([ + perm"(1,2,5,8)(3,12,10,16)(4,14,11,7)(6,15,13,9)", + perm"(1,3)(2,6)(4,15)(5,10)(7,16)(8,13)(9,11)(12,14)", + perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", + perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", + ]), + PermGroup([ + perm"(1,2,5,8)(3,12,10,16)(4,14,11,7)(6,15,13,9)", + perm"(1,3,5,10)(2,6,8,13)(4,15,11,9)(7,16,14,12)", + perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", + perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8)"]), + PermGroup([ + perm"(1,2)(3,13)(4,7)(5,8)(6,10)(9,16)(11,14)(12,15)", + perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)", + perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)", + perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", + ]), + PermGroup([ + perm"(1,2,5,8)(3,13,10,6)(4,7,11,14)(9,16,15,12)", + perm"(1,3,5,10)(2,6,8,13)(4,9,11,15)(7,12,14,16)", + perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)", + perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", + ]), + PermGroup([ + perm"(1,2)(3,13)(4,7)(5,8)(6,10)(9,16)(11,14)(12,15)", + perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)", + perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)", + perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8)"]), + ], + [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)"])], + [ + PermGroup([ + perm"(1,2)(3,18)(4,12)(5,17)(6,9)(7,16)(8,15)(10,14)(11,13)", + perm"(1,3,7,4,8,13,9,14,17)(2,5,10,6,11,15,12,16,18)", + perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11)"]), + PermGroup([ + perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,16)(11,14)(13,18)(15,17)", + perm"(1,3,7)(2,5,10)(4,8,13)(6,11,15)(9,14,17)(12,16,18)", + perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)", + ]), + PermGroup([ + perm"(1,2)(3,10)(4,12)(5,7)(6,9)(8,18)(11,17)(13,16)(14,15)", + perm"(1,3,7)(2,5,10)(4,8,13)(6,11,15)(9,14,17)(12,16,18)", + perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8)"]), + ], + [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)"])], + [ + PermGroup([ + perm"(1,2,3,5)(4,18,7,20)(6,19,9,16)(8,14,11,17)(10,15,13,12)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,20)", + perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)", + ]), + PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9)"]), + PermGroup([ + perm"(1,2,3,5)(4,10,19,17)(6,11,20,12)(7,13,16,14)(8,18,15,9)", + perm"(1,3)(2,5)(4,19)(6,20)(7,16)(8,15)(9,18)(10,17)(11,12)(13,14)", + perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)", + ]), + PermGroup([ + perm"(1,2)(3,5)(4,18)(6,16)(7,20)(8,14)(9,19)(10,12)(11,17)(13,15)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,20)", + perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9)"]), + ], + [ + PermGroup([ + perm"(1,2,4)(3,8,16)(5,10,12)(6,14,7)(9,20,19)(11,21,15)(13,18,17)", + perm"(1,3,6,9,12,15,18)(2,5,8,11,14,17,20)(4,7,10,13,16,19,21)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10)"]), + ], + [ + PermGroup([ + perm"(1,2)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", + perm"(1,3,5,7,9,11,13,15,17,19,21)(2,4,6,8,10,12,14,16,18,20,22)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11,12,13)"]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,6,4,7,9,13)(5,16,10,21,11,22,17,24)(8,18,14,19,15,23,20,12)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", + perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11)"]), + PermGroup([ + perm"(1,2,6)(3,8,20)(4,16,13)(5,9,15)(7,14,10)(11,18,24)(12,23,21)(17,22,19)", + perm"(1,3,5,11)(2,7,9,17)(4,19,12,10)(6,13,15,21)(8,23,18,16)(14,24,22,20)", + perm"(1,4,5,12)(2,8,9,18)(3,10,11,19)(6,14,15,22)(7,16,17,23)(13,20,21,24)", + perm"(1,5)(2,9)(3,11)(4,12)(6,15)(7,17)(8,18)(10,19)(13,21)(14,22)(16,23)(20,24)", + ]), + PermGroup([ + perm"(1,2,4,7)(3,13,9,6)(5,16,11,22)(8,19,15,12)(10,24,17,21)(14,18,20,23)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", + perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,16)(8,12)(9,13)(10,21)(11,22)(14,18)(15,19)(17,24)(20,23)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", + perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", + ]), + PermGroup([ + perm"(1,2)(3,13)(4,7)(5,16)(6,9)(8,12)(10,24)(11,22)(14,23)(15,19)(17,21)(18,20)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", + perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", + ]), + PermGroup([ + perm"(1,2,4,7)(3,6,9,13)(5,16,11,22)(8,19,15,12)(10,21,17,24)(14,23,20,18)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", + perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", + ]), + PermGroup([ + perm"(1,2)(3,13)(4,7)(5,16)(6,9)(8,12)(10,24)(11,22)(14,23)(15,19)(17,21)(18,20)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", + perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9)"]), + PermGroup([ + perm"(1,2)(3,14)(4,7)(5,8)(6,10)(9,21)(11,15)(12,16)(13,18)(17,24)(19,22)(20,23)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)", + perm"(1,4,11)(2,7,15)(3,9,17)(5,12,19)(6,13,20)(8,16,22)(10,18,23)(14,21,24)", + perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,19)(13,21)(15,22)(17,23)(20,24)", + ]), + PermGroup([ + perm"(1,2,5,8)(3,14,10,6)(4,7,12,16)(9,21,18,13)(11,15,19,22)(17,24,23,20)", + perm"(1,3,5,10)(2,6,8,14)(4,9,12,18)(7,13,16,21)(11,17,19,23)(15,20,22,24)", + perm"(1,4,11)(2,7,15)(3,9,17)(5,12,19)(6,13,20)(8,16,22)(10,18,23)(14,21,24)", + perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,19)(13,21)(15,22)(17,23)(20,24)", + ]), + PermGroup([ + perm"(1,2)(3,13)(4,8)(5,7)(6,9)(10,21)(11,20)(12,16)(14,18)(15,17)(19,24)(22,23)", + perm"(1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16)", + perm"(1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24)", + perm"(1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,8)(9,13)(10,14)(11,15)(12,16)(17,20)(18,21)(19,22)(23,24)", + perm"(1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16)", + perm"(1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24)", + perm"(1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,16)(8,12)(9,13)(10,21)(11,22)(14,18)(15,19)(17,24)(20,23)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)", + perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8,9)"]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)", + ]), + PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10)"]), + ], + [ + PermGroup([ + perm"(1,2)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", + perm"(1,3,5,7,9,11,13,15,17,19,21,23,25)(2,4,6,8,10,12,14,16,18,20,22,24,26)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11,12,13,14,15)"]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11,12)"]), + PermGroup([ + perm"(1,2,5)(3,14,25)(4,7,12)(6,19,17)(8,26,24)(9,22,11)(10,15,20)(13,27,16)(18,23,21)", + perm"(1,3,8)(2,6,13)(4,9,16)(5,11,18)(7,14,21)(10,17,23)(12,19,24)(15,22,26)(20,25,27)", + perm"(1,4,10)(2,7,15)(3,9,17)(5,12,20)(6,14,22)(8,16,23)(11,19,25)(13,21,26)(18,24,27)", + ]), + PermGroup([ + perm"(1,2,5,4,7,12,10,15,20)(3,14,25,9,22,11,17,6,19)(8,26,24,16,13,27,23,21,18)", + perm"(1,3,8)(2,6,13)(4,9,16)(5,11,18)(7,14,21)(10,17,23)(12,19,24)(15,22,26)(20,25,27)", + perm"(1,4,10)(2,7,15)(3,9,17)(5,12,20)(6,14,22)(8,16,23)(11,19,25)(13,21,26)(18,24,27)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9)"]), + ], + [ + PermGroup([ + perm"(1,2,3,5)(4,26,7,28)(6,27,9,24)(8,22,11,25)(10,23,13,20)(12,18,15,21)(14,19,17,16)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,28)", + perm"(1,4,8,12,16,20,24)(2,6,10,14,18,22,26)(3,7,11,15,19,23,27)(5,9,13,17,21,25,28)", + ]), + PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11)"]), + PermGroup([ + perm"(1,2)(3,5)(4,26)(6,24)(7,28)(8,22)(9,27)(10,20)(11,25)(12,18)(13,23)(14,16)(15,21)(17,19)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,28)", + perm"(1,4,8,12,16,20,24)(2,6,10,14,18,22,26)(3,7,11,15,19,23,27)(5,9,13,17,21,25,28)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9,10,11)"]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)", + ]), + ], + [ + PermGroup([ + perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,18)(11,15)(13,16)(14,24)(17,21)(19,22)(20,28)(23,26)(25,30)(27,29)", + perm"(1,3,7,13,19)(2,5,10,16,22)(4,8,14,20,25)(6,11,17,23,27)(9,15,21,26,29)(12,18,24,28,30)", + perm"(1,4,9)(2,6,12)(3,8,15)(5,11,18)(7,14,21)(10,17,24)(13,20,26)(16,23,28)(19,25,29)(22,27,30)", + ]), + PermGroup([ + perm"(1,2)(3,5)(4,24)(6,21)(7,10)(8,28)(9,18)(11,26)(12,15)(13,30)(14,23)(16,29)(17,20)(19,27)(22,25)", + perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,27)(21,26,29)(24,28,30)", + perm"(1,4,9,15,21)(2,6,12,18,24)(3,8,14,20,26)(5,11,17,23,28)(7,13,19,25,29)(10,16,22,27,30)", + ]), + PermGroup([ + perm"(1,2)(3,10)(4,24)(5,7)(6,21)(8,30)(9,18)(11,29)(12,15)(13,28)(14,27)(16,26)(17,25)(19,23)(20,22)", + perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,27)(21,26,29)(24,28,30)", + perm"(1,4,9,15,21)(2,6,12,18,24)(3,8,14,20,26)(5,11,17,23,28)(7,13,19,25,29)(10,16,22,27,30)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10)"]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,17,12,27)(4,8,14,20)(6,10,16,22)(7,23,18,11)(13,28,25,32)(15,21,26,30)(19,31,29,24)", + perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,12,16,25)(8,17,21,28)(9,18,22,29)(14,23,26,31)(20,27,30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11,12)"]), + PermGroup([ + perm"(1,2,4,8,6,10,15,21)(3,19,11,28,13,7,24,17)(5,9,14,20,16,22,26,30)(12,29,23,32,25,18,31,27)", + perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,8,14,20,15,21,26,30)(7,23,18,24,19,31,29,11)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,31,18,24)(8,26,20,15)(11,19,23,29)(13,28,25,32)", + perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,21,14,30,15,8,26,20)(7,31,18,11,19,23,29,24)", + perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,21,14,30,15,8,26,20)(7,31,18,11,19,23,29,24)", + perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,25,16,12)(8,17,21,28)(9,29,22,18)(14,31,26,23)(20,32,30,27)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,23,18,11)(8,26,20,15)(13,28,25,32)(19,31,29,24)", + perm"(1,3)(2,7)(4,24)(5,12)(6,13)(8,28)(9,18)(10,19)(11,15)(14,31)(16,25)(17,21)(20,32)(22,29)(23,26)(27,30)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,23,18,11)(8,26,20,15)(13,28,25,32)(19,31,29,24)", + perm"(1,3,6,13)(2,7,10,19)(4,24,15,11)(5,12,16,25)(8,28,21,17)(9,18,22,29)(14,31,26,23)(20,32,30,27)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,21,14,30,15,8,26,20)(7,23,18,24,19,31,29,11)", + perm"(1,3)(2,7)(4,24)(5,12)(6,13)(8,28)(9,18)(10,19)(11,15)(14,31)(16,25)(17,21)(20,32)(22,29)(23,26)(27,30)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,8,14,20,15,21,26,30)(7,23,18,24,19,31,29,11)", + perm"(1,3,4,11)(2,7,8,17)(5,12,14,23)(6,13,15,24)(9,18,20,27)(10,19,21,28)(16,25,26,31)(22,29,30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,23,18,11)(8,26,20,15)(13,28,25,32)(19,31,29,24)", + perm"(1,3,4,11,6,13,15,24)(2,7,8,17,10,19,21,28)(5,12,14,23,16,25,26,31)(9,18,20,27,22,29,30,32)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,23,18,11)(8,26,20,15)(13,28,25,32)(19,31,29,24)", + perm"(1,3,15,24,6,13,4,11)(2,7,21,28,10,19,8,17)(5,12,26,31,16,25,14,23)(9,18,30,32,22,29,20,27)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,21,14,30,15,8,26,20)(7,23,18,24,19,31,29,11)", + perm"(1,3,4,11,6,13,15,24)(2,7,8,17,10,19,21,28)(5,12,14,23,16,25,26,31)(9,18,20,27,22,29,30,32)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18)", + ]), + PermGroup([ + perm"(1,2,4,8,5,9,14,20,6,10,15,21,16,22,26,30)(3,19,11,28,12,29,23,32,13,7,24,17,25,18,31,27)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4,5,14,6,15,16,26)(2,8,9,20,10,21,22,30)(3,11,12,23,13,24,25,31)(7,17,18,27,19,28,29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,17)(4,20)(5,22)(6,10)(7,11)(8,14)(9,16)(12,32)(13,28)(15,30)(18,31)(19,24)(21,26)(23,29)(25,27)", + perm"(1,3)(2,7)(4,23)(5,25)(6,13)(8,27)(9,29)(10,19)(11,14)(12,16)(15,31)(17,20)(18,22)(21,32)(24,26)(28,30)", + perm"(1,4,16,26,6,15,5,14)(2,8,22,30,10,21,9,20)(3,11,25,31,13,24,12,23)(7,17,29,32,19,28,18,27)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,17,13,28)(4,20,15,30)(5,22,16,9)(7,24,19,11)(8,26,21,14)(12,32,25,27)(18,23,29,31)", + perm"(1,3)(2,7)(4,23)(5,25)(6,13)(8,27)(9,29)(10,19)(11,14)(12,16)(15,31)(17,20)(18,22)(21,32)(24,26)(28,30)", + perm"(1,4,16,26,6,15,5,14)(2,8,22,30,10,21,9,20)(3,11,25,31,13,24,12,23)(7,17,29,32,19,28,18,27)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,17,13,28)(4,20,15,30)(5,22,16,9)(7,24,19,11)(8,26,21,14)(12,32,25,27)(18,23,29,31)", + perm"(1,3,6,13)(2,7,10,19)(4,23,15,31)(5,25,16,12)(8,27,21,32)(9,29,22,18)(11,26,24,14)(17,30,28,20)", + perm"(1,4,16,26,6,15,5,14)(2,8,22,30,10,21,9,20)(3,11,25,31,13,24,12,23)(7,17,29,32,19,28,18,27)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6)", perm"(7,8,9,10)"]), + PermGroup([ + perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)", + perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)", + perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)", + perm"(1,4,16,26)(2,8,22,30)(3,11,25,31)(5,14,6,15)(7,17,29,32)(9,20,10,21)(12,23,13,24)(18,27,19,28)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)", + perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,18,12,7)(4,21,14,30)(6,10,16,22)(8,26,20,15)(11,32,23,28)(13,29,25,19)(17,24,27,31)", + perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)", + perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,12,16,25)(8,17,21,28)(9,18,22,29)(14,23,26,31)(20,27,30,32)", + perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,18,12,7)(4,21,14,30)(6,10,16,22)(8,26,20,15)(11,32,23,28)(13,29,25,19)(17,24,27,31)", + perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,12,16,25)(8,17,21,28)(9,18,22,29)(14,23,26,31)(20,27,30,32)", + perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)", + perm"(1,3,16,25)(2,7,22,29)(4,11,26,31)(5,12,6,13)(8,17,30,32)(9,18,10,19)(14,23,15,24)(20,27,21,28)", + perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)", + perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,18,12,7)(4,21,14,30)(6,10,16,22)(8,26,20,15)(11,32,23,28)(13,29,25,19)(17,24,27,31)", + perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9,10,11,12)"]), + PermGroup([ + perm"(1,2,5,9,6,10,16,22)(3,19,12,29,13,7,25,18)(4,8,14,20,15,21,26,30)(11,28,23,32,24,17,31,27)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,5,9,6,10,16,22)(3,7,12,18,13,19,25,29)(4,8,14,20,15,21,26,30)(11,17,23,27,24,28,31,32)", + perm"(1,3)(2,7)(4,24)(5,12)(6,13)(8,28)(9,18)(10,19)(11,15)(14,31)(16,25)(17,21)(20,32)(22,29)(23,26)(27,30)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,8)(5,22)(6,10)(7,12)(9,16)(11,27)(13,29)(14,30)(15,21)(17,23)(19,25)(20,26)(24,32)(28,31)", + perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,22,16,9)(7,25,19,12)(11,27,24,32)(14,30,26,20)(17,31,28,23)", + perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,22,16,9)(7,25,19,12)(11,27,24,32)(14,30,26,20)(17,31,28,23)", + perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,25,16,12)(8,17,21,28)(9,29,22,18)(14,31,26,23)(20,32,30,27)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,8)(5,22)(6,10)(7,12)(9,16)(11,27)(13,29)(14,30)(15,21)(17,23)(19,25)(20,26)(24,32)(28,31)", + perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,22)(6,10)(7,12)(8,15)(9,16)(11,32)(13,29)(14,20)(17,31)(19,25)(23,28)(24,27)(26,30)", + perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,22)(6,10)(7,12)(8,15)(9,16)(11,32)(13,29)(14,20)(17,31)(19,25)(23,28)(24,27)(26,30)", + perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,25,16,12)(8,17,21,28)(9,29,22,18)(14,31,26,23)(20,32,30,27)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8,9,10)"]), + PermGroup([ + perm"(1,2)(3,19)(4,8)(5,9)(6,10)(7,13)(11,28)(12,29)(14,20)(15,21)(16,22)(17,24)(18,25)(23,32)(26,30)(27,31)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,19,13,7)(4,8,15,21)(5,9,16,22)(11,28,24,17)(12,29,25,18)(14,20,26,30)(23,32,31,27)", + perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,12,16,25)(8,17,21,28)(9,18,22,29)(14,23,26,31)(20,27,30,32)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,19)(4,8)(5,9)(6,10)(7,13)(11,28)(12,29)(14,20)(15,21)(16,22)(17,24)(18,25)(23,32)(26,30)(27,31)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,19)(4,8)(5,22)(6,10)(7,13)(9,16)(11,28)(12,18)(14,30)(15,21)(17,24)(20,26)(23,27)(25,29)(31,32)", + perm"(1,3)(2,7)(4,24)(5,12)(6,13)(8,28)(9,18)(10,19)(11,15)(14,31)(16,25)(17,21)(20,32)(22,29)(23,26)(27,30)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)(3,19)(4,8)(5,22)(6,10)(7,13)(9,16)(11,28)(12,18)(14,30)(15,21)(17,24)(20,26)(23,27)(25,29)(31,32)", + perm"(1,3,6,13)(2,7,10,19)(4,24,15,11)(5,12,16,25)(8,28,21,17)(9,18,22,29)(14,31,26,23)(20,32,30,27)", + perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)", + perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4)", + perm"(5,6)", + perm"(7,8)", + perm"(9,10)", + ]), + ], + [PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11,12,13,14)"])], + [ + PermGroup([ + perm"(1,2)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", + perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)", + ]), + ], + [PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10,11,12)"])], + [ + PermGroup([ + perm"(1,2,3,6)(4,27,9,32)(5,18,10,26)(7,29,14,22)(8,21,15,13)(11,17,19,25)(12,16,20,24)(23,34,30,36)(28,35,33,31)", + perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)", + perm"(1,4,11,13,23,31,5,12,22)(2,7,16,18,28,34,8,17,27)(3,9,19,21,30,35,10,20,29)(6,14,24,26,33,36,15,25,32)", + perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)", + ]), + PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11,12,13)"]), + PermGroup([ + perm"(1,2,6,3,7,14,10,17,24)(4,9,27,11,19,34,21,29,36)(5,20,15,12,30,25,22,35,32)(8,16,23,18,26,31,28,33,13)", + perm"(1,3,10)(2,7,17)(4,11,21)(5,12,22)(6,14,24)(8,18,28)(9,19,29)(13,23,31)(15,25,32)(16,26,33)(20,30,35)(27,34,36)", + perm"(1,4)(2,8)(3,11)(5,13)(6,15)(7,18)(9,20)(10,21)(12,23)(14,25)(16,27)(17,28)(19,30)(22,31)(24,32)(26,34)(29,35)(33,36)", + perm"(1,5)(2,9)(3,12)(4,13)(6,16)(7,19)(8,20)(10,22)(11,23)(14,26)(15,27)(17,29)(18,30)(21,31)(24,33)(25,34)(28,35)(32,36)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,27)(5,18)(7,22)(8,13)(9,32)(10,26)(11,17)(12,16)(14,29)(15,21)(19,25)(20,24)(23,34)(28,31)(30,36)(33,35)", + perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)", + perm"(1,4,11,13,23,31,5,12,22)(2,7,16,18,28,34,8,17,27)(3,9,19,21,30,35,10,20,29)(6,14,24,26,33,36,15,25,32)", + perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9,10,11,12,13)"]), + PermGroup([ + perm"(1,2,4,7)(3,6,10,15)(5,18,12,28)(8,23,17,13)(9,14,19,24)(11,27,21,34)(16,31,26,22)(20,33,29,36)(25,35,32,30)", + perm"(1,3,9)(2,6,14)(4,10,19)(5,11,20)(7,15,24)(8,16,25)(12,21,29)(13,22,30)(17,26,32)(18,27,33)(23,31,35)(28,34,36)", + perm"(1,4)(2,7)(3,10)(5,12)(6,15)(8,17)(9,19)(11,21)(13,23)(14,24)(16,26)(18,28)(20,29)(22,31)(25,32)(27,34)(30,35)(33,36)", + perm"(1,5,13)(2,8,18)(3,11,22)(4,12,23)(6,16,27)(7,17,28)(9,20,30)(10,21,31)(14,25,33)(15,26,34)(19,29,35)(24,32,36)", + ]), + PermGroup([ + perm"(1,2,3,6)(4,16,9,24)(5,18,10,26)(7,19,14,11)(8,21,15,13)(12,34,20,36)(17,35,25,31)(22,28,29,33)(23,27,30,32)", + perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)", + perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9,10)"]), + PermGroup([ + perm"(1,2,3,6)(4,28,19,32)(5,34,21,25)(7,30,24,22)(8,35,26,12)(9,33,11,27)(10,36,13,17)(14,23,16,29)(15,31,18,20)", + perm"(1,3)(2,6)(4,19)(5,21)(7,24)(8,26)(9,11)(10,13)(12,35)(14,16)(15,18)(17,36)(20,31)(22,30)(23,29)(25,34)(27,33)(28,32)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)", + perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,18)(8,13)(9,14)(10,26)(11,16)(12,28)(15,21)(17,23)(19,24)(20,33)(22,34)(25,30)(27,31)(29,36)(32,35)", + perm"(1,3)(2,6)(4,19)(5,10)(7,24)(8,15)(9,11)(12,29)(13,21)(14,16)(17,32)(18,26)(20,22)(23,35)(25,27)(28,36)(30,31)(33,34)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)", + perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)", + ]), + PermGroup([ + perm"(1,2,6)(3,7,14)(4,9,27)(5,20,15)(8,16,13)(10,17,24)(11,19,34)(12,30,25)(18,26,23)(21,29,36)(22,35,32)(28,33,31)", + perm"(1,3,10)(2,7,17)(4,11,21)(5,12,22)(6,14,24)(8,18,28)(9,19,29)(13,23,31)(15,25,32)(16,26,33)(20,30,35)(27,34,36)", + perm"(1,4)(2,8)(3,11)(5,13)(6,15)(7,18)(9,20)(10,21)(12,23)(14,25)(16,27)(17,28)(19,30)(22,31)(24,32)(26,34)(29,35)(33,36)", + perm"(1,5)(2,9)(3,12)(4,13)(6,16)(7,19)(8,20)(10,22)(11,23)(14,26)(15,27)(17,29)(18,30)(21,31)(24,33)(25,34)(28,35)(32,36)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,18)(8,13)(9,14)(10,26)(11,16)(12,28)(15,21)(17,23)(19,24)(20,33)(22,34)(25,30)(27,31)(29,36)(32,35)", + perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)", + perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,16)(5,18)(7,11)(8,13)(9,24)(10,26)(12,34)(14,19)(15,21)(17,31)(20,36)(22,28)(23,27)(25,35)(29,33)(30,32)", + perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)", + perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7)", perm"(8,9,10)"]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)", + ]), + ], + [ + PermGroup([ + perm"(1,2)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", + perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)", + ]), + ], + [ + PermGroup([ + perm"(1,2,4)(3,11,31)(5,13,27)(6,20,19)(7,9,29)(8,22,15)(10,18,17)(12,38,34)(14,39,30)(16,36,32)(21,26,37)(23,28,33)(24,35,25)", + perm"(1,3,6,9,12,15,18,21,24,27,30,33,36)(2,5,8,11,14,17,20,23,26,29,32,35,38)(4,7,10,13,16,19,22,25,28,31,34,37,39)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11,12,13,14,15,16)"]), + ], + [ + PermGroup([ + perm"(1,2,3,6,4,7,9,13)(5,32,10,37,11,38,17,40)(8,34,14,35,15,39,21,28)(12,24,18,30,19,31,25,36)(16,26,22,27,23,33,29,20)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,36)(28,34,35,39)(32,37,38,40)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)", + perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)", + ]), + PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10,11,12,13)"]), + PermGroup([ + perm"(1,2,3,6,4,7,9,13)(5,16,34,30,11,23,39,36)(8,18,37,27,15,25,40,20)(10,22,35,31,17,29,28,24)(12,32,26,14,19,38,33,21)", + perm"(1,3,4,9)(2,6,7,13)(5,34,11,39)(8,37,15,40)(10,35,17,28)(12,26,19,33)(14,38,21,32)(16,30,23,36)(18,27,25,20)(22,31,29,24)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)", + perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)", + ]), + PermGroup([ + perm"(1,2,4,7)(3,13,9,6)(5,32,11,38)(8,35,15,28)(10,40,17,37)(12,24,19,31)(14,34,21,39)(16,27,23,20)(18,36,25,30)(22,26,29,33)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,36)(28,34,35,39)(32,37,38,40)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)", + perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,32)(8,28)(9,13)(10,37)(11,38)(12,24)(14,34)(15,35)(16,20)(17,40)(18,30)(19,31)(21,39)(22,26)(23,27)(25,36)(29,33)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,36)(28,34,35,39)(32,37,38,40)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)", + perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)", + ]), + PermGroup([ + perm"(1,2)(3,13)(4,7)(5,32)(6,9)(8,28)(10,40)(11,38)(12,24)(14,39)(15,35)(16,20)(17,37)(18,36)(19,31)(21,34)(22,33)(23,27)(25,30)(26,29)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,36)(28,34,35,39)(32,37,38,40)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)", + perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)", + ]), + PermGroup([ + perm"(1,2,4,7)(3,6,9,13)(5,32,11,38)(8,35,15,28)(10,37,17,40)(12,24,19,31)(14,39,21,34)(16,27,23,20)(18,30,25,36)(22,33,29,26)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)", + perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)", + ]), + PermGroup([ + perm"(1,2)(3,13)(4,7)(5,32)(6,9)(8,28)(10,40)(11,38)(12,24)(14,39)(15,35)(16,20)(17,37)(18,36)(19,31)(21,34)(22,33)(23,27)(25,30)(26,29)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)", + perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6)", perm"(7,8,9,10,11)"]), + PermGroup([ + perm"(1,2)(3,14)(4,7)(5,8)(6,10)(9,22)(11,15)(12,16)(13,18)(17,30)(19,23)(20,24)(21,26)(25,37)(27,31)(28,32)(29,34)(33,40)(35,38)(36,39)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)", + perm"(1,4,11,19,27)(2,7,15,23,31)(3,9,17,25,33)(5,12,20,28,35)(6,13,21,29,36)(8,16,24,32,38)(10,18,26,34,39)(14,22,30,37,40)", + perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,20)(13,22)(15,24)(17,26)(19,28)(21,30)(23,32)(25,34)(27,35)(29,37)(31,38)(33,39)(36,40)", + ]), + PermGroup([ + perm"(1,2,5,8)(3,14,10,6)(4,7,12,16)(9,22,18,13)(11,15,20,24)(17,30,26,21)(19,23,28,32)(25,37,34,29)(27,31,35,38)(33,40,39,36)", + perm"(1,3,5,10)(2,6,8,14)(4,9,12,18)(7,13,16,22)(11,17,20,26)(15,21,24,30)(19,25,28,34)(23,29,32,37)(27,33,35,39)(31,36,38,40)", + perm"(1,4,11,19,27)(2,7,15,23,31)(3,9,17,25,33)(5,12,20,28,35)(6,13,21,29,36)(8,16,24,32,38)(10,18,26,34,39)(14,22,30,37,40)", + perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,20)(13,22)(15,24)(17,26)(19,28)(21,30)(23,32)(25,34)(27,35)(29,37)(31,38)(33,39)(36,40)", + ]), + PermGroup([ + perm"(1,2,4,7)(3,6,9,13)(5,16,35,31)(8,19,38,20)(10,22,39,36)(11,23,28,24)(12,32,27,15)(14,25,40,26)(17,29,34,30)(18,37,33,21)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)", + perm"(1,4)(2,7)(3,9)(5,35)(6,13)(8,38)(10,39)(11,28)(12,27)(14,40)(15,32)(16,31)(17,34)(18,33)(19,20)(21,37)(22,36)(23,24)(25,26)(29,30)", + perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,32)(8,28)(9,13)(10,37)(11,38)(12,24)(14,34)(15,35)(16,20)(17,40)(18,30)(19,31)(21,39)(22,26)(23,27)(25,36)(29,33)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)", + perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8,9,10,11)"]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)", + ]), + ], + [ + PermGroup([ + perm"(1,2)(3,5)(4,36)(6,33)(7,10)(8,40)(9,30)(11,38)(12,27)(13,42)(14,35)(15,24)(16,41)(17,32)(18,21)(19,39)(20,29)(22,37)(23,26)(25,34)(28,31)", + perm"(1,3,7)(2,5,10)(4,14,31)(6,17,34)(8,19,21)(9,26,13)(11,22,24)(12,29,16)(15,38,37)(18,40,39)(20,41,27)(23,42,30)(25,33,32)(28,36,35)", + perm"(1,4,9,15,21,27,33)(2,6,12,18,24,30,36)(3,8,14,20,26,32,38)(5,11,17,23,29,35,40)(7,13,19,25,31,37,41)(10,16,22,28,34,39,42)", + ]), + PermGroup([ + perm"(1,2)(3,5)(4,6)(7,10)(8,11)(9,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,28)(26,29)(27,30)(31,34)(32,35)(33,36)(37,39)(38,40)(41,42)", + perm"(1,3,7)(2,5,10)(4,14,31)(6,17,34)(8,19,21)(9,26,13)(11,22,24)(12,29,16)(15,38,37)(18,40,39)(20,41,27)(23,42,30)(25,33,32)(28,36,35)", + perm"(1,4,9,15,21,27,33)(2,6,12,18,24,30,36)(3,8,14,20,26,32,38)(5,11,17,23,29,35,40)(7,13,19,25,31,37,41)(10,16,22,28,34,39,42)", + ]), + PermGroup([ + perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,18)(11,15)(13,16)(14,24)(17,21)(19,22)(20,30)(23,27)(25,28)(26,36)(29,33)(31,34)(32,40)(35,38)(37,42)(39,41)", + perm"(1,3,7,13,19,25,31)(2,5,10,16,22,28,34)(4,8,14,20,26,32,37)(6,11,17,23,29,35,39)(9,15,21,27,33,38,41)(12,18,24,30,36,40,42)", + perm"(1,4,9)(2,6,12)(3,8,15)(5,11,18)(7,14,21)(10,17,24)(13,20,27)(16,23,30)(19,26,33)(22,29,36)(25,32,38)(28,35,40)(31,37,41)(34,39,42)", + ]), + PermGroup([ + perm"(1,2)(3,5)(4,36)(6,33)(7,10)(8,40)(9,30)(11,38)(12,27)(13,42)(14,35)(15,24)(16,41)(17,32)(18,21)(19,39)(20,29)(22,37)(23,26)(25,34)(28,31)", + perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,28)(21,26,31)(24,29,34)(27,32,37)(30,35,39)(33,38,41)(36,40,42)", + perm"(1,4,9,15,21,27,33)(2,6,12,18,24,30,36)(3,8,14,20,26,32,38)(5,11,17,23,29,35,40)(7,13,19,25,31,37,41)(10,16,22,28,34,39,42)", + ]), + PermGroup([ + perm"(1,2)(3,10)(4,36)(5,7)(6,33)(8,42)(9,30)(11,41)(12,27)(13,40)(14,39)(15,24)(16,38)(17,37)(18,21)(19,35)(20,34)(22,32)(23,31)(25,29)(26,28)", + perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,28)(21,26,31)(24,29,34)(27,32,37)(30,35,39)(33,38,41)(36,40,42)", + perm"(1,4,9,15,21,27,33)(2,6,12,18,24,30,36)(3,8,14,20,26,32,38)(5,11,17,23,29,35,40)(7,13,19,25,31,37,41)(10,16,22,28,34,39,42)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10,11,12)"]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,5)(4,42,7,44)(6,43,9,40)(8,38,11,41)(10,39,13,36)(12,34,15,37)(14,35,17,32)(16,30,19,33)(18,31,21,28)(20,26,23,29)(22,27,25,24)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,41)(40,43)(42,44)", + perm"(1,4,8,12,16,20,24,28,32,36,40)(2,6,10,14,18,22,26,30,34,38,42)(3,7,11,15,19,23,27,31,35,39,43)(5,9,13,17,21,25,29,33,37,41,44)", + ]), + PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11,12,13,14,15)"]), + PermGroup([ + perm"(1,2)(3,5)(4,42)(6,40)(7,44)(8,38)(9,43)(10,36)(11,41)(12,34)(13,39)(14,32)(15,37)(16,30)(17,35)(18,28)(19,33)(20,26)(21,31)(22,24)(23,29)(25,27)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,41)(40,43)(42,44)", + perm"(1,4,8,12,16,20,24,28,32,36,40)(2,6,10,14,18,22,26,30,34,38,42)(3,7,11,15,19,23,27,31,35,39,43)(5,9,13,17,21,25,29,33,37,41,44)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4)", + perm"(5,6,7,8,9,10,11,12,13,14,15)", + ]), + ], + [ + PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10,11,12,13,14)"]), + PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9,10,11)"]), + ], + [ + PermGroup([ + perm"(1,2)(3,46)(4,45)(5,44)(6,43)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)", + perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,7,4,8,11,18,5,9,12,19,14,21,25,32)(6,24,13,35,15,37,26,44,16,38,27,45,29,46,39,48)(10,28,20,30,22,40,33,31,23,41,34,42,36,47,43,17)", + perm"(1,3,4,11,5,12,14,25)(2,7,8,18,9,19,21,32)(6,13,15,26,16,27,29,39)(10,20,22,33,23,34,36,43)(17,28,30,40,31,41,42,47)(24,35,37,44,38,45,46,48)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,3)", + perm"(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)", + ]), + PermGroup([ + perm"(1,2,7)(3,9,44)(4,39,18)(5,11,37)(6,27,20)(8,19,29)(10,21,17)(12,40,35)(13,26,43)(14,41,48)(15,22,45)(16,38,33)(23,36,28)(24,46,42)(25,32,30)(31,47,34)", + perm"(1,3,17,30)(2,8,27,40)(4,12,31,42)(5,13,6,14)(7,18,37,45)(9,22,41,47)(10,23,11,24)(15,28,16,29)(19,32,46,48)(20,33,21,34)(25,38,26,39)(35,43,36,44)", + perm"(1,4,5,15)(2,9,10,25)(3,12,13,28)(6,16,17,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,32,33,43)(21,36,37,46)(24,39,40,47)(34,44,45,48)", + perm"(1,5)(2,10)(3,13)(4,15)(6,17)(7,20)(8,23)(9,25)(11,27)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(22,38)(24,40)(26,41)(29,42)(32,43)(34,45)(36,46)(39,47)(44,48)", + perm"(1,6)(2,11)(3,14)(4,16)(5,17)(7,21)(8,24)(9,26)(10,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,39)(23,40)(25,41)(28,42)(32,44)(33,45)(35,46)(38,47)(43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)", + perm"(1,3,4,11,5,12,14,25)(2,7,8,18,9,19,21,32)(6,13,15,26,16,27,29,39)(10,20,22,33,23,34,36,43)(17,28,30,40,31,41,42,47)(24,35,37,44,38,45,46,48)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,19)(4,8)(5,9)(6,24)(7,12)(10,17)(11,32)(13,45)(14,21)(15,37)(16,38)(18,25)(20,41)(22,30)(23,31)(26,48)(27,35)(28,34)(29,46)(33,47)(36,42)(39,44)(40,43)", + perm"(1,3,4,11,5,12,14,25)(2,7,8,18,9,19,21,32)(6,13,15,26,16,27,29,39)(10,20,22,33,23,34,36,43)(17,28,30,40,31,41,42,47)(24,35,37,44,38,45,46,48)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,24)(7,11)(8,14)(10,17)(12,32)(13,44)(15,46)(16,38)(19,25)(20,40)(22,42)(23,31)(26,35)(27,48)(28,33)(29,37)(30,36)(34,47)(39,45)(41,43)", + perm"(1,3,4,11,5,12,14,25)(2,7,8,18,9,19,21,32)(6,13,15,26,16,27,29,39)(10,20,22,33,23,34,36,43)(17,28,30,40,31,41,42,47)(24,35,37,44,38,45,46,48)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,24)(7,11)(8,14)(10,17)(12,32)(13,44)(15,46)(16,38)(19,25)(20,40)(22,42)(23,31)(26,35)(27,48)(28,33)(29,37)(30,36)(34,47)(39,45)(41,43)", + perm"(1,3,14,25,5,12,4,11)(2,7,21,32,9,19,8,18)(6,13,29,39,16,27,15,26)(10,20,36,43,23,34,22,33)(17,28,42,47,31,41,30,40)(24,35,46,48,38,45,37,44)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,18,12,32)(4,21,14,8)(6,24,16,38)(7,25,19,11)(10,31,23,17)(13,44,27,48)(15,46,29,37)(20,47,34,40)(22,30,36,42)(26,35,39,45)(28,33,41,43)", + perm"(1,3,14,25,5,12,4,11)(2,7,21,32,9,19,8,18)(6,13,29,39,16,27,15,26)(10,20,36,43,23,34,22,33)(17,28,42,47,31,41,30,40)(24,35,46,48,38,45,37,44)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,4,8,5,9,14,21)(3,7,11,18,12,19,25,32)(6,24,15,37,16,38,29,46)(10,30,22,31,23,42,36,17)(13,35,26,44,27,45,39,48)(20,40,33,41,34,47,43,28)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,4,8,5,9,14,21)(3,19,11,32,12,7,25,18)(6,24,15,37,16,38,29,46)(10,30,22,31,23,42,36,17)(13,45,26,48,27,35,39,44)(20,47,33,28,34,40,43,41)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,4,8)(3,7,11,18)(5,9,14,21)(6,24,15,37)(10,30,22,17)(12,19,25,32)(13,35,26,44)(16,38,29,46)(20,40,33,28)(23,42,36,31)(27,45,39,48)(34,47,43,41)", + perm"(1,3,5,12)(2,7,9,19)(4,11,14,25)(6,13,16,27)(8,18,21,32)(10,20,23,34)(15,26,29,39)(17,28,31,41)(22,33,36,43)(24,35,38,45)(30,40,42,47)(37,44,46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,19,12,7)(4,8,14,21)(6,24,16,38)(10,31,23,17)(11,32,25,18)(13,45,27,35)(15,37,29,46)(20,28,34,41)(22,42,36,30)(26,48,39,44)(33,40,43,47)", + perm"(1,3,4,11)(2,7,8,18)(5,12,14,25)(6,13,15,26)(9,19,21,32)(10,20,22,33)(16,27,29,39)(17,28,30,40)(23,34,36,43)(24,35,37,44)(31,41,42,47)(38,45,46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,4,8)(3,19,11,32)(5,9,14,21)(6,24,15,37)(7,25,18,12)(10,30,22,17)(13,45,26,48)(16,38,29,46)(20,47,33,41)(23,42,36,31)(27,35,39,44)(28,34,40,43)", + perm"(1,3,5,12)(2,7,9,19)(4,11,14,25)(6,13,16,27)(8,18,21,32)(10,20,23,34)(15,26,29,39)(17,28,31,41)(22,33,36,43)(24,35,38,45)(30,40,42,47)(37,44,46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,19)(4,8)(5,9)(6,24)(7,12)(10,17)(11,32)(13,45)(14,21)(15,37)(16,38)(18,25)(20,41)(22,30)(23,31)(26,48)(27,35)(28,34)(29,46)(33,47)(36,42)(39,44)(40,43)", + perm"(1,3,4,11)(2,7,8,18)(5,12,14,25)(6,13,15,26)(9,19,21,32)(10,20,22,33)(16,27,29,39)(17,28,30,40)(23,34,36,43)(24,35,37,44)(31,41,42,47)(38,45,46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,24)(7,11)(8,14)(10,17)(12,32)(13,44)(15,46)(16,38)(19,25)(20,40)(22,42)(23,31)(26,35)(27,48)(28,33)(29,37)(30,36)(34,47)(39,45)(41,43)", + perm"(1,3)(2,7)(4,25)(5,12)(6,13)(8,32)(9,19)(10,20)(11,14)(15,39)(16,27)(17,28)(18,21)(22,43)(23,34)(24,35)(26,29)(30,47)(31,41)(33,36)(37,48)(38,45)(40,42)(44,46)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,18,12,32)(4,21,14,8)(6,24,16,38)(7,25,19,11)(10,31,23,17)(13,44,27,48)(15,46,29,37)(20,47,34,40)(22,30,36,42)(26,35,39,45)(28,33,41,43)", + perm"(1,3)(2,7)(4,25)(5,12)(6,13)(8,32)(9,19)(10,20)(11,14)(15,39)(16,27)(17,28)(18,21)(22,43)(23,34)(24,35)(26,29)(30,47)(31,41)(33,36)(37,48)(38,45)(40,42)(44,46)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,21)(5,9)(6,24)(7,11)(8,14)(10,17)(12,32)(13,44)(15,46)(16,38)(19,25)(20,40)(22,42)(23,31)(26,35)(27,48)(28,33)(29,37)(30,36)(34,47)(39,45)(41,43)", + perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,18,12,32)(4,21,14,8)(6,24,16,38)(7,25,19,11)(10,31,23,17)(13,44,27,48)(15,46,29,37)(20,47,34,40)(22,30,36,42)(26,35,39,45)(28,33,41,43)", + perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,4,8)(3,19,11,32)(5,9,14,21)(6,24,15,37)(7,25,18,12)(10,30,22,17)(13,45,26,48)(16,38,29,46)(20,47,33,41)(23,42,36,31)(27,35,39,44)(28,34,40,43)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6,7)", perm"(8,9,10,11)"]), + PermGroup([ + perm"(1,2,6,10)(3,19,13,35)(4,8,16,23)(5,9,17,24)(7,28,20,12)(11,33,27,45)(14,21,30,37)(15,22,31,38)(18,41,34,26)(25,43,40,48)(29,36,42,46)(32,47,44,39)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)", + perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)", + perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,19,13,35)(4,8,16,23)(5,9,17,24)(7,28,20,12)(11,33,27,45)(14,21,30,37)(15,22,31,38)(18,41,34,26)(25,43,40,48)(29,36,42,46)(32,47,44,39)", + perm"(1,3,5,12)(2,7,9,19)(4,11,15,26)(6,13,17,28)(8,18,22,33)(10,20,24,35)(14,25,29,39)(16,27,31,41)(21,32,36,43)(23,34,38,45)(30,40,42,47)(37,44,46,48)", + perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)", + perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)", + perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10,11,12,13)"]), + PermGroup([ + perm"(1,2,5,9,6,10,17,24)(3,20,12,35,13,7,28,19)(4,8,15,22,16,23,31,38)(11,34,26,45,27,18,41,33)(14,21,29,36,30,37,42,46)(25,44,39,48,40,32,47,43)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)", + perm"(1,5,6,17)(2,9,10,24)(3,12,13,28)(4,15,16,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,33,34,45)(21,36,37,46)(25,39,40,47)(32,43,44,48)", + perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2)(3,19)(4,8)(5,24)(6,10)(7,12)(9,17)(11,33)(13,35)(14,21)(15,38)(16,23)(18,26)(20,28)(22,31)(25,43)(27,45)(29,46)(30,37)(32,39)(34,41)(36,42)(40,48)(44,47)", + perm"(1,3)(2,7)(4,11)(5,28)(6,13)(8,18)(9,35)(10,20)(12,17)(14,25)(15,41)(16,27)(19,24)(21,32)(22,45)(23,34)(26,31)(29,47)(30,40)(33,38)(36,48)(37,44)(39,42)(43,46)", + perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)", + perm"(1,5,6,17)(2,9,10,24)(3,12,13,28)(4,15,16,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,33,34,45)(21,36,37,46)(25,39,40,47)(32,43,44,48)", + perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,19,13,35)(4,8,16,23)(5,24,17,9)(7,28,20,12)(11,33,27,45)(14,21,30,37)(15,38,31,22)(18,41,34,26)(25,43,40,48)(29,46,42,36)(32,47,44,39)", + perm"(1,3)(2,7)(4,11)(5,28)(6,13)(8,18)(9,35)(10,20)(12,17)(14,25)(15,41)(16,27)(19,24)(21,32)(22,45)(23,34)(26,31)(29,47)(30,40)(33,38)(36,48)(37,44)(39,42)(43,46)", + perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)", + perm"(1,5,6,17)(2,9,10,24)(3,12,13,28)(4,15,16,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,33,34,45)(21,36,37,46)(25,39,40,47)(32,43,44,48)", + perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,19,13,35)(4,8,16,23)(5,24,17,9)(7,28,20,12)(11,33,27,45)(14,21,30,37)(15,38,31,22)(18,41,34,26)(25,43,40,48)(29,46,42,36)(32,47,44,39)", + perm"(1,3,6,13)(2,7,10,20)(4,11,16,27)(5,28,17,12)(8,18,23,34)(9,35,24,19)(14,25,30,40)(15,41,31,26)(21,32,37,44)(22,45,38,33)(29,47,42,39)(36,48,46,43)", + perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)", + perm"(1,5,6,17)(2,9,10,24)(3,12,13,28)(4,15,16,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,33,34,45)(21,36,37,46)(25,39,40,47)(32,43,44,48)", + perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,18,14,34)(4,9,16,24)(5,8,17,23)(7,27,21,11)(12,33,29,45)(13,32,30,44)(15,38,31,22)(19,41,36,26)(20,40,37,25)(28,48,42,43)(35,39,46,47)", + perm"(1,3,11)(2,7,18)(4,30,47)(5,28,40)(6,14,27)(8,37,48)(9,35,44)(10,21,34)(12,41,31)(13,39,16)(15,29,26)(17,42,25)(19,45,38)(20,43,23)(22,36,33)(24,46,32)", + perm"(1,4,6,16)(2,8,10,23)(3,12,14,29)(5,31,17,15)(7,19,21,36)(9,38,24,22)(11,25,27,40)(13,42,30,28)(18,32,34,44)(20,46,37,35)(26,47,41,39)(33,48,45,43)", + perm"(1,5,6,17)(2,9,10,24)(3,13,14,30)(4,15,16,31)(7,20,21,37)(8,22,23,38)(11,26,27,41)(12,28,29,42)(18,33,34,45)(19,35,36,46)(25,39,40,47)(32,43,44,48)", + perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2)(3,18)(4,9)(5,8)(6,10)(7,11)(12,33)(13,32)(14,34)(15,38)(16,24)(17,23)(19,26)(20,25)(21,27)(22,31)(28,48)(29,45)(30,44)(35,47)(36,41)(37,40)(39,46)(42,43)", + perm"(1,3,11)(2,7,18)(4,30,47)(5,28,40)(6,14,27)(8,37,48)(9,35,44)(10,21,34)(12,41,31)(13,39,16)(15,29,26)(17,42,25)(19,45,38)(20,43,23)(22,36,33)(24,46,32)", + perm"(1,4,6,16)(2,8,10,23)(3,12,14,29)(5,31,17,15)(7,19,21,36)(9,38,24,22)(11,25,27,40)(13,42,30,28)(18,32,34,44)(20,46,37,35)(26,47,41,39)(33,48,45,43)", + perm"(1,5,6,17)(2,9,10,24)(3,13,14,30)(4,15,16,31)(7,20,21,37)(8,22,23,38)(11,26,27,41)(12,28,29,42)(18,33,34,45)(19,35,36,46)(25,39,40,47)(32,43,44,48)", + perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,3,7)(4,21,11,32)(5,10,12,20)(6,9,13,19)(8,25,18,14)(15,37,26,44)(16,36,27,43)(17,24,28,35)(22,40,33,30)(23,39,34,29)(31,46,41,48)(38,47,45,42)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,14)(2,8,21)(3,11,25)(5,16,42)(6,31,29)(7,18,32)(9,23,46)(10,38,36)(12,27,47)(13,41,39)(15,30,17)(19,34,48)(20,45,43)(22,37,24)(26,40,28)(33,44,35)", + perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)", + perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,4,8)(3,7,12,19)(5,9,15,22)(6,10,16,23)(11,18,25,32)(13,20,28,35)(14,21,29,36)(17,24,31,38)(26,33,39,43)(27,34,40,44)(30,37,42,46)(41,45,47,48)", + perm"(1,3,11)(2,7,18)(4,12,25)(5,14,41)(6,30,26)(8,19,32)(9,21,45)(10,37,33)(13,27,17)(15,29,47)(16,42,39)(20,34,24)(22,36,48)(23,46,43)(28,40,31)(35,44,38)", + perm"(1,4)(2,8)(3,12)(5,15)(6,16)(7,19)(9,22)(10,23)(11,25)(13,28)(14,29)(17,31)(18,32)(20,35)(21,36)(24,38)(26,39)(27,40)(30,42)(33,43)(34,44)(37,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,13)(4,15)(6,17)(7,20)(8,22)(10,24)(11,26)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(23,38)(25,39)(27,41)(29,42)(32,43)(34,45)(36,46)(40,47)(44,48)", + perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,8)(5,9)(6,10)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(17,24)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)(39,43)(40,44)(41,45)(42,46)(47,48)", + perm"(1,3,11)(2,7,18)(4,13,39)(5,28,25)(6,14,27)(8,20,43)(9,35,32)(10,21,34)(12,26,15)(16,30,47)(17,42,40)(19,33,22)(23,37,48)(24,46,44)(29,41,31)(36,45,38)", + perm"(1,4,6,16)(2,8,10,23)(3,12,14,29)(5,31,17,15)(7,19,21,36)(9,38,24,22)(11,25,27,40)(13,42,30,28)(18,32,34,44)(20,46,37,35)(26,47,41,39)(33,48,45,43)", + perm"(1,5,6,17)(2,9,10,24)(3,13,14,30)(4,15,16,31)(7,20,21,37)(8,22,23,38)(11,26,27,41)(12,28,29,42)(18,33,34,45)(19,35,36,46)(25,39,40,47)(32,43,44,48)", + perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,7,14,21)(4,8,16,23)(5,9,17,24)(11,18,27,34)(12,19,29,36)(13,20,30,37)(15,22,31,38)(25,32,40,44)(26,33,41,45)(28,35,42,46)(39,43,47,48)", + perm"(1,3,11)(2,7,18)(4,13,39)(5,28,25)(6,14,27)(8,20,43)(9,35,32)(10,21,34)(12,26,15)(16,30,47)(17,42,40)(19,33,22)(23,37,48)(24,46,44)(29,41,31)(36,45,38)", + perm"(1,4,6,16)(2,8,10,23)(3,12,14,29)(5,31,17,15)(7,19,21,36)(9,38,24,22)(11,25,27,40)(13,42,30,28)(18,32,34,44)(20,46,37,35)(26,47,41,39)(33,48,45,43)", + perm"(1,5,6,17)(2,9,10,24)(3,13,14,30)(4,15,16,31)(7,20,21,37)(8,22,23,38)(11,26,27,41)(12,28,29,42)(18,33,34,45)(19,35,36,46)(25,39,40,47)(32,43,44,48)", + perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,7,12,19)(4,21,14,8)(6,24,16,38)(10,31,23,17)(11,32,25,18)(13,35,27,45)(15,46,29,37)(20,41,34,28)(22,30,36,42)(26,48,39,44)(33,40,43,47)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)", + perm"(1,3,5,12)(2,7,9,19)(4,11,14,25)(6,13,16,27)(8,18,21,32)(10,20,23,34)(15,26,29,39)(17,28,31,41)(22,33,36,43)(24,35,38,45)(30,40,42,47)(37,44,46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)", + perm"(1,3)(2,7)(4,25)(5,12)(6,13)(8,32)(9,19)(10,20)(11,14)(15,39)(16,27)(17,28)(18,21)(22,43)(23,34)(24,35)(26,29)(30,47)(31,41)(33,36)(37,48)(38,45)(40,42)(44,46)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)", + perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)", + perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)", + perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)", + perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2,5,9)(3,7,12,19)(4,8,14,21)(6,24,16,38)(10,31,23,17)(11,18,25,32)(13,35,27,45)(15,37,29,46)(20,41,34,28)(22,42,36,30)(26,44,39,48)(33,47,43,40)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7)", perm"(8,9,10,11)"]), + PermGroup([ + perm"(1,2)(3,20)(4,8)(5,9)(6,10)(7,13)(11,33)(12,35)(14,21)(15,22)(16,23)(17,24)(18,26)(19,28)(25,44)(27,45)(29,36)(30,37)(31,38)(32,40)(34,41)(39,48)(42,46)(43,47)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5,16)(2,9,23)(3,12,27)(4,14,29)(6,17,31)(7,19,34)(8,21,36)(10,24,38)(11,25,39)(13,28,41)(15,30,42)(18,32,43)(20,35,45)(22,37,46)(26,40,47)(33,44,48)", + perm"(1,6)(2,10)(3,13)(4,15)(5,17)(7,20)(8,22)(9,24)(11,26)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(23,38)(25,40)(27,41)(29,42)(32,44)(34,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,6,10)(3,20,13,7)(4,8,15,22)(5,9,17,24)(11,33,26,18)(12,35,28,19)(14,21,30,37)(16,23,31,38)(25,44,40,32)(27,45,41,34)(29,36,42,46)(39,48,47,43)", + perm"(1,3,6,13)(2,7,10,20)(4,11,15,26)(5,12,17,28)(8,18,22,33)(9,19,24,35)(14,25,30,40)(16,27,31,41)(21,32,37,44)(23,34,38,45)(29,39,42,47)(36,43,46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5,16)(2,9,23)(3,12,27)(4,14,29)(6,17,31)(7,19,34)(8,21,36)(10,24,38)(11,25,39)(13,28,41)(15,30,42)(18,32,43)(20,35,45)(22,37,46)(26,40,47)(33,44,48)", + perm"(1,6)(2,10)(3,13)(4,15)(5,17)(7,20)(8,22)(9,24)(11,26)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(23,38)(25,40)(27,41)(29,42)(32,44)(34,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2)(3,20)(4,8)(5,9)(6,10)(7,13)(11,33)(12,35)(14,21)(15,22)(16,23)(17,24)(18,26)(19,28)(25,44)(27,45)(29,36)(30,37)(31,38)(32,40)(34,41)(39,48)(42,46)(43,47)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,6,15)(2,8,10,22)(3,11,13,26)(5,14,17,30)(7,18,20,33)(9,21,24,37)(12,25,28,40)(16,29,31,42)(19,32,35,44)(23,36,38,46)(27,39,41,47)(34,43,45,48)", + perm"(1,5,16)(2,9,23)(3,12,27)(4,14,29)(6,17,31)(7,19,34)(8,21,36)(10,24,38)(11,25,39)(13,28,41)(15,30,42)(18,32,43)(20,35,45)(22,37,46)(26,40,47)(33,44,48)", + perm"(1,6)(2,10)(3,13)(4,15)(5,17)(7,20)(8,22)(9,24)(11,26)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(23,38)(25,40)(27,41)(29,42)(32,44)(34,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,21)(5,10)(6,9)(8,14)(11,32)(12,20)(13,19)(15,37)(16,36)(17,24)(18,25)(22,30)(23,29)(26,44)(27,43)(28,35)(31,46)(33,40)(34,39)(38,42)(41,48)(45,47)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,14)(2,8,21)(3,11,25)(5,16,42)(6,31,29)(7,18,32)(9,23,46)(10,38,36)(12,27,47)(13,41,39)(15,30,17)(19,34,48)(20,45,43)(22,37,24)(26,40,28)(33,44,35)", + perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)", + perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,8)(5,9)(6,10)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(17,24)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)(39,43)(40,44)(41,45)(42,46)(47,48)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4,14)(2,8,21)(3,11,25)(5,16,42)(6,31,29)(7,18,32)(9,23,46)(10,38,36)(12,27,47)(13,41,39)(15,30,17)(19,34,48)(20,45,43)(22,37,24)(26,40,28)(33,44,35)", + perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)", + perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)", + ]), + PermGroup([ + perm"(1,2,7)(3,9,32)(4,22,18)(5,11,37)(6,27,20)(8,19,12)(10,21,17)(13,26,48)(14,41,43)(15,39,45)(16,47,33)(23,36,42)(24,46,28)(25,44,30)(29,40,35)(31,38,34)", + perm"(1,3)(2,8)(4,12)(5,13)(6,14)(7,18)(9,22)(10,23)(11,24)(15,28)(16,29)(17,30)(19,32)(20,33)(21,34)(25,38)(26,39)(27,40)(31,42)(35,43)(36,44)(37,45)(41,47)(46,48)", + perm"(1,4)(2,9)(3,12)(5,15)(6,16)(7,19)(8,22)(10,25)(11,26)(13,28)(14,29)(17,31)(18,32)(20,35)(21,36)(23,38)(24,39)(27,41)(30,42)(33,43)(34,44)(37,46)(40,47)(45,48)", + perm"(1,5)(2,10)(3,13)(4,15)(6,17)(7,20)(8,23)(9,25)(11,27)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(22,38)(24,40)(26,41)(29,42)(32,43)(34,45)(36,46)(39,47)(44,48)", + perm"(1,6)(2,11)(3,14)(4,16)(5,17)(7,21)(8,24)(9,26)(10,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,39)(23,40)(25,41)(28,42)(32,44)(33,45)(35,46)(38,47)(43,48)", + ]), + PermGroup([ + perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)", + perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)", + perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)", + perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)", + perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4)", + perm"(5,6)", + perm"(7,8)", + perm"(9,10,11)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49)", + ]), + PermGroup([perm"(1,2,3,4,5,6,7)", perm"(8,9,10,11,12,13,14)"]), + ], + [ + PermGroup([ + perm"(1,2)(3,50)(4,30)(5,49)(6,25)(7,48)(8,47)(9,20)(10,46)(11,45)(12,16)(13,44)(14,43)(15,42)(17,41)(18,40)(19,39)(21,38)(22,37)(23,36)(24,35)(26,34)(27,33)(28,32)(29,31)", + perm"(1,3,7,13,21,4,8,14,22,31,9,15,23,32,39,16,24,33,40,45,25,34,41,46,49)(2,5,10,17,26,6,11,18,27,35,12,19,28,36,42,20,29,37,43,47,30,38,44,48,50)", + perm"(1,4,9,16,25)(2,6,12,20,30)(3,8,15,24,34)(5,11,19,29,38)(7,14,23,33,41)(10,18,28,37,44)(13,22,32,40,46)(17,27,36,43,48)(21,31,39,45,49)(26,35,42,47,50)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)", + ]), + PermGroup([ + perm"(1,2)(3,5)(4,30)(6,25)(7,10)(8,38)(9,20)(11,34)(12,16)(13,17)(14,44)(15,29)(18,41)(19,24)(21,26)(22,48)(23,37)(27,46)(28,33)(31,50)(32,43)(35,49)(36,40)(39,47)(42,45)", + perm"(1,3,7,13,21)(2,5,10,17,26)(4,8,14,22,31)(6,11,18,27,35)(9,15,23,32,39)(12,19,28,36,42)(16,24,33,40,45)(20,29,37,43,47)(25,34,41,46,49)(30,38,44,48,50)", + perm"(1,4,9,16,25)(2,6,12,20,30)(3,8,15,24,34)(5,11,19,29,38)(7,14,23,33,41)(10,18,28,37,44)(13,22,32,40,46)(17,27,36,43,48)(21,31,39,45,49)(26,35,42,47,50)", + ]), + PermGroup([ + perm"(1,2)(3,26)(4,30)(5,21)(6,25)(7,17)(8,50)(9,20)(10,13)(11,49)(12,16)(14,48)(15,47)(18,46)(19,45)(22,44)(23,43)(24,42)(27,41)(28,40)(29,39)(31,38)(32,37)(33,36)(34,35)", + perm"(1,3,7,13,21)(2,5,10,17,26)(4,8,14,22,31)(6,11,18,27,35)(9,15,23,32,39)(12,19,28,36,42)(16,24,33,40,45)(20,29,37,43,47)(25,34,41,46,49)(30,38,44,48,50)", + perm"(1,4,9,16,25)(2,6,12,20,30)(3,8,15,24,34)(5,11,19,29,38)(7,14,23,33,41)(10,18,28,37,44)(13,22,32,40,46)(17,27,36,43,48)(21,31,39,45,49)(26,35,42,47,50)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6,7)", perm"(8,9,10,11,12)"]), + ], + [ + PermGroup([ + perm"(1,2,3)", + perm"(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,5)(4,50,7,52)(6,51,9,48)(8,46,11,49)(10,47,13,44)(12,42,15,45)(14,43,17,40)(16,38,19,41)(18,39,21,36)(20,34,23,37)(22,35,25,32)(24,30,27,33)(26,31,29,28)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,41)(40,43)(42,45)(44,47)(46,49)(48,51)(50,52)", + perm"(1,4,8,12,16,20,24,28,32,36,40,44,48)(2,6,10,14,18,22,26,30,34,38,42,46,50)(3,7,11,15,19,23,27,31,35,39,43,47,51)(5,9,13,17,21,25,29,33,37,41,45,49,52)", + ]), + PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11,12,13,14,15,16,17)"]), + PermGroup([ + perm"(1,2,3,5)(4,34,51,25)(6,35,52,20)(7,37,48,22)(8,14,47,45)(9,32,50,23)(10,15,49,40)(11,17,44,42)(12,46,43,13)(16,26,39,33)(18,27,41,28)(19,29,36,30)(21,24,38,31)", + perm"(1,3)(2,5)(4,51)(6,52)(7,48)(8,47)(9,50)(10,49)(11,44)(12,43)(13,46)(14,45)(15,40)(16,39)(17,42)(18,41)(19,36)(20,35)(21,38)(22,37)(23,32)(24,31)(25,34)(26,33)(27,28)(29,30)", + perm"(1,4,8,12,16,20,24,28,32,36,40,44,48)(2,6,10,14,18,22,26,30,34,38,42,46,50)(3,7,11,15,19,23,27,31,35,39,43,47,51)(5,9,13,17,21,25,29,33,37,41,45,49,52)", + ]), + PermGroup([ + perm"(1,2)(3,5)(4,50)(6,48)(7,52)(8,46)(9,51)(10,44)(11,49)(12,42)(13,47)(14,40)(15,45)(16,38)(17,43)(18,36)(19,41)(20,34)(21,39)(22,32)(23,37)(24,30)(25,35)(26,28)(27,33)(29,31)", + perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,41)(40,43)(42,45)(44,47)(46,49)(48,51)(50,52)", + perm"(1,4,8,12,16,20,24,28,32,36,40,44,48)(2,6,10,14,18,22,26,30,34,38,42,46,50)(3,7,11,15,19,23,27,31,35,39,43,47,51)(5,9,13,17,21,25,29,33,37,41,45,49,52)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4)", + perm"(5,6,7,8,9,10,11,12,13,14,15,16,17)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)", + ]), + ], + [ + PermGroup([ + perm"(1,2)(3,28)(4,33)(5,20)(6,21)(7,26)(8,14)(9,16)(10,15)(11,51)(12,19)(13,18)(17,48)(22,45)(23,50)(24,43)(25,42)(27,46)(29,39)(30,47)(31,37)(32,36)(34,40)(35,44)(38,41)(49,54)(52,53)", + perm"(1,3,9,26,38,47,13,24,36,5,11,22,40,49,53,27,39,48,14,25,37,12,23,35,4,10,21)(2,6,15,33,44,50,19,31,42,8,17,29,46,52,54,34,45,51,20,32,43,18,30,41,7,16,28)", + perm"(1,4,12,14,27,40,5,13,26)(2,7,18,20,34,46,8,19,33)(3,10,23,25,39,49,11,24,38)(6,16,30,32,45,52,17,31,44)(9,21,35,37,48,53,22,36,47)(15,28,41,43,51,54,29,42,50)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,33)(5,20)(7,26)(8,14)(9,15)(10,44)(11,32)(12,19)(13,18)(16,38)(17,25)(21,50)(22,43)(23,31)(24,30)(27,46)(28,47)(29,37)(34,40)(35,42)(36,41)(39,52)(45,49)(48,54)(51,53)", + perm"(1,3,9)(2,6,15)(4,10,21)(5,11,22)(7,16,28)(8,17,29)(12,23,35)(13,24,36)(14,25,37)(18,30,41)(19,31,42)(20,32,43)(26,38,47)(27,39,48)(33,44,50)(34,45,51)(40,49,53)(46,52,54)", + perm"(1,4,12,14,27,40,5,13,26)(2,7,18,20,34,46,8,19,33)(3,10,23,25,39,49,11,24,38)(6,16,30,32,45,52,17,31,44)(9,21,35,37,48,53,22,36,47)(15,28,41,43,51,54,29,42,50)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,20)(8,14)(9,15)(10,16)(11,32)(12,18)(13,34)(17,25)(19,27)(21,28)(22,43)(23,30)(24,45)(26,46)(29,37)(31,39)(33,40)(35,41)(36,51)(38,52)(42,48)(44,49)(47,54)(50,53)", + perm"(1,3,9,4,10,21,12,23,35)(2,6,15,7,16,28,18,30,41)(5,11,22,13,24,36,26,38,47)(8,17,29,19,31,42,33,44,50)(14,25,37,27,39,48,40,49,53)(20,32,43,34,45,51,46,52,54)", + perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,18)(5,20)(7,12)(8,14)(9,15)(10,30)(11,32)(13,46)(16,23)(17,25)(19,40)(21,41)(22,43)(24,52)(26,34)(27,33)(28,35)(29,37)(31,49)(36,54)(38,45)(39,44)(42,53)(47,51)(48,50)", + perm"(1,3,9)(2,6,15)(4,24,48)(5,11,22)(7,31,51)(8,17,29)(10,36,27)(12,49,47)(13,39,21)(14,25,37)(16,42,34)(18,52,50)(19,45,28)(20,32,43)(23,53,26)(30,54,33)(35,40,38)(41,46,44)", + perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,33)(5,20)(7,26)(8,14)(9,15)(10,44)(11,32)(12,19)(13,18)(16,38)(17,25)(21,50)(22,43)(23,31)(24,30)(27,46)(28,47)(29,37)(34,40)(35,42)(36,41)(39,52)(45,49)(48,54)(51,53)", + perm"(1,3,9)(2,6,15)(4,24,48)(5,11,22)(7,31,51)(8,17,29)(10,36,27)(12,49,47)(13,39,21)(14,25,37)(16,42,34)(18,52,50)(19,45,28)(20,32,43)(23,53,26)(30,54,33)(35,40,38)(41,46,44)", + perm"(1,4,12,14,27,40,5,13,26)(2,7,18,20,34,46,8,19,33)(3,10,23,25,39,49,11,24,38)(6,16,30,32,45,52,17,31,44)(9,21,35,37,48,53,22,36,47)(15,28,41,43,51,54,29,42,50)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)(3,29)(4,18)(5,20)(6,22)(7,12)(8,14)(9,17)(10,50)(11,15)(13,46)(16,47)(19,40)(21,44)(23,42)(24,41)(25,43)(26,34)(27,33)(28,38)(30,36)(31,35)(32,37)(39,54)(45,53)(48,52)(49,51)", + perm"(1,3,9,14,25,37,5,11,22)(2,6,15,20,32,43,8,17,29)(4,10,21,27,39,48,13,24,36)(7,16,28,34,45,51,19,31,42)(12,23,35,40,49,53,26,38,47)(18,30,41,46,52,54,33,44,50)", + perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)(3,15)(4,18)(5,8)(6,9)(7,12)(10,41)(11,29)(13,33)(14,20)(16,35)(17,22)(19,26)(21,30)(23,28)(24,50)(25,43)(27,46)(31,47)(32,37)(34,40)(36,44)(38,42)(39,54)(45,53)(48,52)(49,51)", + perm"(1,3,9)(2,6,15)(4,24,48)(5,11,22)(7,31,51)(8,17,29)(10,36,27)(12,49,47)(13,39,21)(14,25,37)(16,42,34)(18,52,50)(19,45,28)(20,32,43)(23,53,26)(30,54,33)(35,40,38)(41,46,44)", + perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10,11,12,13,14)"]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,8)(9,15)(10,16)(11,17)(12,18)(13,19)(14,20)(21,28)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(35,41)(36,42)(37,43)(38,44)(39,45)(40,46)(47,50)(48,51)(49,52)(53,54)", + perm"(1,3,9)(2,6,15)(4,24,48)(5,11,22)(7,31,51)(8,17,29)(10,36,27)(12,49,47)(13,39,21)(14,25,37)(16,42,34)(18,52,50)(19,45,28)(20,32,43)(23,53,26)(30,54,33)(35,40,38)(41,46,44)", + perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,8)(9,15)(10,16)(11,17)(12,18)(13,19)(14,20)(21,28)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(35,41)(36,42)(37,43)(38,44)(39,45)(40,46)(47,50)(48,51)(49,52)(53,54)", + perm"(1,3,9,5,11,22,14,25,37)(2,6,15,8,17,29,20,32,43)(4,24,48,13,39,21,27,10,36)(7,31,51,19,45,28,34,16,42)(12,49,47,26,23,53,40,38,35)(18,52,50,33,30,54,46,44,41)", + perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,20)(8,14)(9,15)(10,16)(11,32)(12,18)(13,34)(17,25)(19,27)(21,28)(22,43)(23,30)(24,45)(26,46)(29,37)(31,39)(33,40)(35,41)(36,51)(38,52)(42,48)(44,49)(47,54)(50,53)", + perm"(1,3,9)(2,6,15)(4,10,21)(5,11,22)(7,16,28)(8,17,29)(12,23,35)(13,24,36)(14,25,37)(18,30,41)(19,31,42)(20,32,43)(26,38,47)(27,39,48)(33,44,50)(34,45,51)(40,49,53)(46,52,54)", + perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,18)(5,20)(7,12)(8,14)(9,15)(10,30)(11,32)(13,46)(16,23)(17,25)(19,40)(21,41)(22,43)(24,52)(26,34)(27,33)(28,35)(29,37)(31,49)(36,54)(38,45)(39,44)(42,53)(47,51)(48,50)", + perm"(1,3,9)(2,6,15)(4,10,21)(5,11,22)(7,16,28)(8,17,29)(12,23,35)(13,24,36)(14,25,37)(18,30,41)(19,31,42)(20,32,43)(26,38,47)(27,39,48)(33,44,50)(34,45,51)(40,49,53)(46,52,54)", + perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([ + perm"(1,2)(3,15)(4,18)(5,20)(6,9)(7,12)(8,14)(10,41)(11,43)(13,46)(16,35)(17,37)(19,40)(21,30)(22,32)(23,28)(24,54)(25,29)(26,34)(27,33)(31,53)(36,52)(38,51)(39,50)(42,49)(44,48)(45,47)", + perm"(1,3,9)(2,6,15)(4,10,21)(5,11,22)(7,16,28)(8,17,29)(12,23,35)(13,24,36)(14,25,37)(18,30,41)(19,31,42)(20,32,43)(26,38,47)(27,39,48)(33,44,50)(34,45,51)(40,49,53)(46,52,54)", + perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)", + perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8)", perm"(9,10,11)"]), + ], + [ + PermGroup([ + perm"(1,2,4,7,11)(3,19,28,51,26)(5,23,32,53,10)(6,39,52,42,41)(8,27,36,40,14)(9,43,54,46,25)(12,31,20,44,18)(13,47,55,30,29)(15,24,48,22,16)(17,50,45,34,33)(21,35,49,38,37)", + perm"(1,3,6,10,15,20,25,30,35,40,45)(2,5,9,14,19,24,29,34,39,44,49)(4,8,13,18,23,28,33,38,43,48,52)(7,12,17,22,27,32,37,42,47,51,54)(11,16,21,26,31,36,41,46,50,53,55)", + ]), + PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10,11,12,13,14,15,16)"]), + ], + [ + PermGroup([ + perm"(1,2,3,6,4,7,9,13)(5,48,10,53,11,54,17,56)(8,50,14,51,15,55,21,44)(12,40,18,46,19,47,25,52)(16,42,22,43,23,49,29,36)(20,32,26,38,27,39,33,45)(24,34,30,35,31,41,37,28)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,37)(28,34,35,41)(32,38,39,45)(36,42,43,49)(40,46,47,52)(44,50,51,55)(48,53,54,56)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)", + perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)", + ]), + PermGroup([perm"(1,2,3,4,5,6,7)", perm"(8,9,10,11,12,13,14,15)"]), + PermGroup([ + perm"(1,2,4,7)(3,13,9,6)(5,48,11,54)(8,51,15,44)(10,56,17,53)(12,40,19,47)(14,50,21,55)(16,43,23,36)(18,52,25,46)(20,32,27,39)(22,42,29,49)(24,35,31,28)(26,45,33,38)(30,34,37,41)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,37)(28,34,35,41)(32,38,39,45)(36,42,43,49)(40,46,47,52)(44,50,51,55)(48,53,54,56)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)", + perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,48)(8,44)(9,13)(10,53)(11,54)(12,40)(14,50)(15,51)(16,36)(17,56)(18,46)(19,47)(20,32)(21,55)(22,42)(23,43)(24,28)(25,52)(26,38)(27,39)(29,49)(30,34)(31,35)(33,45)(37,41)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,37)(28,34,35,41)(32,38,39,45)(36,42,43,49)(40,46,47,52)(44,50,51,55)(48,53,54,56)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)", + perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)", + ]), + PermGroup([ + perm"(1,2)(3,13)(4,7)(5,48)(6,9)(8,44)(10,56)(11,54)(12,40)(14,55)(15,51)(16,36)(17,53)(18,52)(19,47)(20,32)(21,50)(22,49)(23,43)(24,28)(25,46)(26,45)(27,39)(29,42)(30,41)(31,35)(33,38)(34,37)", + perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,37)(28,34,35,41)(32,38,39,45)(36,42,43,49)(40,46,47,52)(44,50,51,55)(48,53,54,56)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)", + perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)", + ]), + PermGroup([ + perm"(1,2,4,7)(3,6,9,13)(5,48,11,54)(8,51,15,44)(10,53,17,56)(12,40,19,47)(14,55,21,50)(16,43,23,36)(18,46,25,52)(20,32,27,39)(22,49,29,42)(24,35,31,28)(26,38,33,45)(30,41,37,34)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,37)(32,38)(35,41)(36,42)(39,45)(40,46)(43,49)(44,50)(47,52)(48,53)(51,55)(54,56)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)", + perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)", + ]), + PermGroup([ + perm"(1,2)(3,13)(4,7)(5,48)(6,9)(8,44)(10,56)(11,54)(12,40)(14,55)(15,51)(16,36)(17,53)(18,52)(19,47)(20,32)(21,50)(22,49)(23,43)(24,28)(25,46)(26,45)(27,39)(29,42)(30,41)(31,35)(33,38)(34,37)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,37)(32,38)(35,41)(36,42)(39,45)(40,46)(43,49)(44,50)(47,52)(48,53)(51,55)(54,56)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)", + perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)", + ]), + PermGroup([perm"(1,2)", perm"(3,4,5,6)", perm"(7,8,9,10,11,12,13)"]), + PermGroup([ + perm"(1,2)(3,14)(4,7)(5,8)(6,10)(9,22)(11,15)(12,16)(13,18)(17,30)(19,23)(20,24)(21,26)(25,38)(27,31)(28,32)(29,34)(33,46)(35,39)(36,40)(37,42)(41,53)(43,47)(44,48)(45,50)(49,56)(51,54)(52,55)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,37)(32,38)(35,41)(36,42)(39,45)(40,46)(43,49)(44,50)(47,52)(48,53)(51,55)(54,56)", + perm"(1,4,11,19,27,35,43)(2,7,15,23,31,39,47)(3,9,17,25,33,41,49)(5,12,20,28,36,44,51)(6,13,21,29,37,45,52)(8,16,24,32,40,48,54)(10,18,26,34,42,50,55)(14,22,30,38,46,53,56)", + perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,20)(13,22)(15,24)(17,26)(19,28)(21,30)(23,32)(25,34)(27,36)(29,38)(31,40)(33,42)(35,44)(37,46)(39,48)(41,50)(43,51)(45,53)(47,54)(49,55)(52,56)", + ]), + PermGroup([ + perm"(1,2,5,8)(3,14,10,6)(4,7,12,16)(9,22,18,13)(11,15,20,24)(17,30,26,21)(19,23,28,32)(25,38,34,29)(27,31,36,40)(33,46,42,37)(35,39,44,48)(41,53,50,45)(43,47,51,54)(49,56,55,52)", + perm"(1,3,5,10)(2,6,8,14)(4,9,12,18)(7,13,16,22)(11,17,20,26)(15,21,24,30)(19,25,28,34)(23,29,32,38)(27,33,36,42)(31,37,40,46)(35,41,44,50)(39,45,48,53)(43,49,51,55)(47,52,54,56)", + perm"(1,4,11,19,27,35,43)(2,7,15,23,31,39,47)(3,9,17,25,33,41,49)(5,12,20,28,36,44,51)(6,13,21,29,37,45,52)(8,16,24,32,40,48,54)(10,18,26,34,42,50,55)(14,22,30,38,46,53,56)", + perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,20)(13,22)(15,24)(17,26)(19,28)(21,30)(23,32)(25,34)(27,36)(29,38)(31,40)(33,42)(35,44)(37,46)(39,48)(41,50)(43,51)(45,53)(47,54)(49,55)(52,56)", + ]), + PermGroup([ + perm"(1,2,6,13,21,29,37)(3,8,16,34,51,48,54)(4,9,26,44,41,50,45)(5,18,36,33,43,38,46)(7,15,24,42,55,52,12)(10,19,14,23,32,49,56)(11,28,25,35,30,39,47)(17,27,22,31,40,53,20)", + perm"(1,3)(2,7)(4,10)(5,11)(6,14)(8,17)(9,18)(12,20)(13,22)(15,25)(16,26)(19,28)(21,30)(23,33)(24,34)(27,36)(29,38)(31,41)(32,42)(35,44)(37,45)(39,48)(40,49)(43,51)(46,52)(47,53)(50,55)(54,56)", + perm"(1,4)(2,8)(3,10)(5,12)(6,15)(7,17)(9,19)(11,20)(13,23)(14,25)(16,27)(18,28)(21,31)(22,33)(24,35)(26,36)(29,39)(30,41)(32,43)(34,44)(37,46)(38,48)(40,50)(42,51)(45,52)(47,54)(49,55)(53,56)", + perm"(1,5)(2,9)(3,11)(4,12)(6,16)(7,18)(8,19)(10,20)(13,24)(14,26)(15,27)(17,28)(21,32)(22,34)(23,35)(25,36)(29,40)(30,42)(31,43)(33,44)(37,47)(38,49)(39,50)(41,51)(45,53)(46,54)(48,55)(52,56)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,48)(8,44)(9,13)(10,53)(11,54)(12,40)(14,50)(15,51)(16,36)(17,56)(18,46)(19,47)(20,32)(21,55)(22,42)(23,43)(24,28)(25,52)(26,38)(27,39)(29,49)(30,34)(31,35)(33,45)(37,41)", + perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,37)(32,38)(35,41)(36,42)(39,45)(40,46)(43,49)(44,50)(47,52)(48,53)(51,55)(54,56)", + perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)", + perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4)", + perm"(5,6)", + perm"(7,8,9,10,11,12,13)", + ]), + ], + [ + PermGroup([ + perm"(1,2,4)(3,23,37)(5,25,33)(6,44,13)(7,21,35)(8,46,9)(10,42,11)(12,29,22)(14,31,18)(15,50,55)(16,27,20)(17,52,51)(19,48,53)(24,56,40)(26,57,36)(28,54,38)(30,41,49)(32,43,45)(34,39,47)", + perm"(1,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54)(2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47,50,53,56)(4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55,57)", + ]), + PermGroup([ + perm"(1,2,3)", + perm"(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)", + ]), + ], + [ + PermGroup([ + perm"(1,2)(3,58)(4,57)(5,56)(6,55)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)", + perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59)", + ]), + ], + [ + PermGroup([ + perm"(1,2,4,7)(3,6,10,15)(5,18,12,30)(8,24,17,13)(9,14,20,26)(11,29,22,42)(16,36,28,23)(19,25,32,38)(21,41,34,52)(27,47,40,35)(31,37,43,48)(33,51,45,58)(39,55,50,46)(44,57,53,60)(49,59,56,54)", + perm"(1,3,9,19,31)(2,6,14,25,37)(4,10,20,32,43)(5,11,21,33,44)(7,15,26,38,48)(8,16,27,39,49)(12,22,34,45,53)(13,23,35,46,54)(17,28,40,50,56)(18,29,41,51,57)(24,36,47,55,59)(30,42,52,58,60)", + perm"(1,4)(2,7)(3,10)(5,12)(6,15)(8,17)(9,20)(11,22)(13,24)(14,26)(16,28)(18,30)(19,32)(21,34)(23,36)(25,38)(27,40)(29,42)(31,43)(33,45)(35,47)(37,48)(39,50)(41,52)(44,53)(46,55)(49,56)(51,58)(54,59)(57,60)", + perm"(1,5,13)(2,8,18)(3,11,23)(4,12,24)(6,16,29)(7,17,30)(9,21,35)(10,22,36)(14,27,41)(15,28,42)(19,33,46)(20,34,47)(25,39,51)(26,40,52)(31,44,54)(32,45,55)(37,49,57)(38,50,58)(43,53,59)(48,56,60)", + ]), + PermGroup([ + perm"(1,2,4,7)(3,6,10,15)(5,42,12,52)(8,47,17,36)(9,14,19,25)(11,51,21,58)(13,30,23,41)(16,55,27,46)(18,35,29,24)(20,57,31,60)(22,40,33,50)(26,59,37,54)(28,45,39,34)(32,49,43,56)(38,53,48,44)", + perm"(1,3,9)(2,6,14)(4,10,19)(5,11,20)(7,15,25)(8,16,26)(12,21,31)(13,22,32)(17,27,37)(18,28,38)(23,33,43)(24,34,44)(29,39,48)(30,40,49)(35,45,53)(36,46,54)(41,50,56)(42,51,57)(47,55,59)(52,58,60)", + perm"(1,4)(2,7)(3,10)(5,12)(6,15)(8,17)(9,19)(11,21)(13,23)(14,25)(16,27)(18,29)(20,31)(22,33)(24,35)(26,37)(28,39)(30,41)(32,43)(34,45)(36,47)(38,48)(40,50)(42,52)(44,53)(46,55)(49,56)(51,58)(54,59)(57,60)", + perm"(1,5,13,24,36)(2,8,18,30,42)(3,11,22,34,46)(4,12,23,35,47)(6,16,28,40,51)(7,17,29,41,52)(9,20,32,44,54)(10,21,33,45,55)(14,26,38,49,57)(15,27,39,50,58)(19,31,43,53,59)(25,37,48,56,60)", + ]), + PermGroup([ + perm"(1,2,3,6)(4,16,9,25)(5,42,10,50)(7,19,14,11)(8,45,15,36)(12,58,20,60)(13,30,21,39)(17,59,26,55)(18,33,27,24)(22,52,31,57)(23,51,32,56)(28,54,37,47)(29,53,38,46)(34,41,43,49)(35,40,44,48)", + perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,25)(17,26)(18,27)(22,31)(23,32)(24,33)(28,37)(29,38)(30,39)(34,43)(35,44)(36,45)(40,48)(41,49)(42,50)(46,53)(47,54)(51,56)(52,57)(55,59)(58,60)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)", + perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6,7)", perm"(8,9,10,11,12)"]), + PermGroup([perm"(1,2,3,4,5)", perm"(1,2,3)"]), + PermGroup([ + perm"(1,2,4,7)(3,6,10,15)(5,18,47,41)(8,23,52,24)(9,14,19,25)(11,28,55,50)(12,29,36,30)(13,42,35,17)(16,33,58,34)(20,38,59,56)(21,39,46,40)(22,51,45,27)(26,43,60,44)(31,48,54,49)(32,57,53,37)", + perm"(1,3,9)(2,6,14)(4,10,19)(5,11,20)(7,15,25)(8,16,26)(12,21,31)(13,22,32)(17,27,37)(18,28,38)(23,33,43)(24,34,44)(29,39,48)(30,40,49)(35,45,53)(36,46,54)(41,50,56)(42,51,57)(47,55,59)(52,58,60)", + perm"(1,4)(2,7)(3,10)(5,47)(6,15)(8,52)(9,19)(11,55)(12,36)(13,35)(14,25)(16,58)(17,42)(18,41)(20,59)(21,46)(22,45)(23,24)(26,60)(27,51)(28,50)(29,30)(31,54)(32,53)(33,34)(37,57)(38,56)(39,40)(43,44)(48,49)", + perm"(1,5,13,24,36)(2,8,18,30,42)(3,11,22,34,46)(4,12,23,35,47)(6,16,28,40,51)(7,17,29,41,52)(9,20,32,44,54)(10,21,33,45,55)(14,26,38,49,57)(15,27,39,50,58)(19,31,43,53,59)(25,37,48,56,60)", + ]), + PermGroup([ + perm"(1,2,3,6)(4,16,9,25)(5,30,45,27)(7,19,14,11)(8,33,50,13)(10,39,36,18)(12,51,54,48)(15,24,42,21)(17,53,57,34)(20,56,47,40)(22,41,59,38)(23,28,44,60)(26,46,52,43)(29,31,49,55)(32,37,35,58)", + perm"(1,3)(2,6)(4,9)(5,45)(7,14)(8,50)(10,36)(11,19)(12,54)(13,33)(15,42)(16,25)(17,57)(18,39)(20,47)(21,24)(22,59)(23,44)(26,52)(27,30)(28,60)(29,49)(31,55)(32,35)(34,53)(37,58)(38,41)(40,56)(43,46)(48,51)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)", + perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,42)(8,36)(9,14)(10,50)(11,16)(12,52)(13,30)(15,45)(17,47)(18,24)(19,25)(20,57)(21,39)(22,58)(23,41)(26,54)(27,33)(28,55)(29,35)(31,60)(32,49)(34,51)(37,59)(38,44)(40,46)(43,56)(48,53)", + perm"(1,3)(2,6)(4,19)(5,10)(7,25)(8,15)(9,11)(12,31)(13,21)(14,16)(17,37)(18,27)(20,22)(23,43)(24,33)(26,28)(29,48)(30,39)(32,34)(35,53)(36,45)(38,40)(41,56)(42,50)(44,46)(47,59)(49,51)(52,60)(54,55)(57,58)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)", + perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)", + ]), + PermGroup([ + perm"(1,2,6)(3,7,14)(4,9,28)(5,20,15)(8,16,13)(10,17,25)(11,19,40)(12,32,26)(18,27,24)(21,29,37)(22,31,51)(23,44,38)(30,39,36)(33,41,48)(34,43,58)(35,54,49)(42,50,47)(45,53,60)(46,59,56)(52,57,55)", + perm"(1,3,10,21,33)(2,7,17,29,41)(4,11,22,34,45)(5,12,23,35,46)(6,14,25,37,48)(8,18,30,42,52)(9,19,31,43,53)(13,24,36,47,55)(15,26,38,49,56)(16,27,39,50,57)(20,32,44,54,59)(28,40,51,58,60)", + perm"(1,4)(2,8)(3,11)(5,13)(6,15)(7,18)(9,20)(10,22)(12,24)(14,26)(16,28)(17,30)(19,32)(21,34)(23,36)(25,38)(27,40)(29,42)(31,44)(33,45)(35,47)(37,49)(39,51)(41,52)(43,54)(46,55)(48,56)(50,58)(53,59)(57,60)", + perm"(1,5)(2,9)(3,12)(4,13)(6,16)(7,19)(8,20)(10,23)(11,24)(14,27)(15,28)(17,31)(18,32)(21,35)(22,36)(25,39)(26,40)(29,43)(30,44)(33,46)(34,47)(37,50)(38,51)(41,53)(42,54)(45,55)(48,57)(49,58)(52,59)(56,60)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,42)(8,36)(9,14)(10,50)(11,16)(12,52)(13,30)(15,45)(17,47)(18,24)(19,25)(20,57)(21,39)(22,58)(23,41)(26,54)(27,33)(28,55)(29,35)(31,60)(32,49)(34,51)(37,59)(38,44)(40,46)(43,56)(48,53)", + perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,25)(17,26)(18,27)(22,31)(23,32)(24,33)(28,37)(29,38)(30,39)(34,43)(35,44)(36,45)(40,48)(41,49)(42,50)(46,53)(47,54)(51,56)(52,57)(55,59)(58,60)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)", + perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,7)(5,18)(8,13)(9,14)(10,27)(11,16)(12,30)(15,21)(17,24)(19,25)(20,39)(22,28)(23,42)(26,33)(29,36)(31,37)(32,50)(34,40)(35,52)(38,45)(41,47)(43,48)(44,57)(46,58)(49,54)(51,55)(53,60)(56,59)", + perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,25)(17,26)(18,27)(22,31)(23,32)(24,33)(28,37)(29,38)(30,39)(34,43)(35,44)(36,45)(40,48)(41,49)(42,50)(46,53)(47,54)(51,56)(52,57)(55,59)(58,60)", + perm"(1,4,11,22,34)(2,7,16,28,40)(3,9,19,31,43)(5,12,23,35,46)(6,14,25,37,48)(8,17,29,41,51)(10,20,32,44,53)(13,24,36,47,55)(15,26,38,49,56)(18,30,42,52,58)(21,33,45,54,59)(27,39,50,57,60)", + perm"(1,5,13)(2,8,18)(3,10,21)(4,12,24)(6,15,27)(7,17,30)(9,20,33)(11,23,36)(14,26,39)(16,29,42)(19,32,45)(22,35,47)(25,38,50)(28,41,52)(31,44,54)(34,46,55)(37,49,57)(40,51,58)(43,53,59)(48,56,60)", + ]), + PermGroup([ + perm"(1,2)(3,6)(4,16)(5,42)(7,11)(8,36)(9,25)(10,50)(12,58)(13,30)(14,19)(15,45)(17,55)(18,24)(20,60)(21,39)(22,52)(23,51)(26,59)(27,33)(28,47)(29,46)(31,57)(32,56)(34,41)(35,40)(37,54)(38,53)(43,49)(44,48)", + perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,25)(17,26)(18,27)(22,31)(23,32)(24,33)(28,37)(29,38)(30,39)(34,43)(35,44)(36,45)(40,48)(41,49)(42,50)(46,53)(47,54)(51,56)(52,57)(55,59)(58,60)", + perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)", + perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4)", + perm"(5,6,7)", + perm"(8,9,10,11,12)", + ]), + ], + [ + PermGroup([ + perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61)", + ]), + ], + [ + PermGroup([ + perm"(1,2)(3,62)(4,61)(5,60)(6,59)(7,58)(8,57)(9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)", + perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62)", + ]), + PermGroup([ + perm"(1,2)", + perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33)", + ]), + ], + [ + PermGroup([ + perm"(1,2,5,3,6,11,8,13,19)(4,15,39,9,23,47,16,31,54)(7,21,35,14,29,43,22,37,27)(10,33,12,17,41,20,25,49,28)(18,51,48,26,58,55,34,62,60)(24,56,44,32,61,52,40,63,36)(30,53,50,38,59,57,46,45,42)", + perm"(1,3,8)(2,6,13)(4,9,16)(5,11,19)(7,14,22)(10,17,25)(12,20,28)(15,23,31)(18,26,34)(21,29,37)(24,32,40)(27,35,43)(30,38,46)(33,41,49)(36,44,52)(39,47,54)(42,50,57)(45,53,59)(48,55,60)(51,58,62)(56,61,63)", + perm"(1,4,10,18,27,36,45)(2,7,15,24,33,42,51)(3,9,17,26,35,44,53)(5,12,21,30,39,48,56)(6,14,23,32,41,50,58)(8,16,25,34,43,52,59)(11,20,29,38,47,55,61)(13,22,31,40,49,57,62)(19,28,37,46,54,60,63)", + ]), + PermGroup([perm"(1,2,3,4,5,6,7)", perm"(8,9,10,11,12,13,14,15,16)"]), + PermGroup([ + perm"(1,2,5)(3,6,11)(4,15,39)(7,21,27)(8,13,19)(9,23,47)(10,33,12)(14,29,35)(16,31,54)(17,41,20)(18,51,48)(22,37,43)(24,56,36)(25,49,28)(26,58,55)(30,45,42)(32,61,44)(34,62,60)(38,53,50)(40,63,52)(46,59,57)", + perm"(1,3,8)(2,6,13)(4,9,16)(5,11,19)(7,14,22)(10,17,25)(12,20,28)(15,23,31)(18,26,34)(21,29,37)(24,32,40)(27,35,43)(30,38,46)(33,41,49)(36,44,52)(39,47,54)(42,50,57)(45,53,59)(48,55,60)(51,58,62)(56,61,63)", + perm"(1,4,10,18,27,36,45)(2,7,15,24,33,42,51)(3,9,17,26,35,44,53)(5,12,21,30,39,48,56)(6,14,23,32,41,50,58)(8,16,25,34,43,52,59)(11,20,29,38,47,55,61)(13,22,31,40,49,57,62)(19,28,37,46,54,60,63)", + ]), + PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9,10,11,12,13)"]), + ], +]