TWOCOHOM: Thorough test: Construct perfect groups

tst/testextra/makeperfect.g

@@ -0,0 +1,81 @@
+# construct perfect groups of given order
+
+Practice:=function(n) #makes perfect
+local isot,res,resp,d,i,j,nt,p,e,q,cf,m,coh,v,new,quot,nts,pf,pl,comp,reps;
+ isot:=function(g,h)
+ local c,d;
+ if Collected(List(ConjugacyClasses(g),
+ x->[Order(Representative(x)),Size(x)]))<>
+ Collected(List(ConjugacyClasses(h),
+ x->[Order(Representative(x)),Size(x)])) then return false;
+ fi;
+ if Collected(List(MaximalSubgroupClassReps(g),Size))<>
+ Collected(List(MaximalSubgroupClassReps(h),Size)) then return false;
+ fi;
+ if Collected(List(NormalSubgroups(g),
+ x->[Size(x),IsAbelian(x),Size(Centralizer(g,x))]))<>
+ Collected(List(NormalSubgroups(h),
+ x->[Size(x),IsAbelian(x),Size(Centralizer(h,x))])) then return false;
+ fi;
+ c:=CharacterTable(g);;Irr(c);
+ d:=CharacterTable(h);;Irr(d);
+ if TransformingPermutationsCharacterTables(c,d)=fail then return false;fi;
+ return IsomorphismGroups(g,h)<>fail;
+ end;
+
+ res:=[];
+ resp:=[];
+ d:=Filtered(DivisorsInt(n),x->x<n);
+ for i in d do
+ nts:=n/i;
+ if IsPrimePowerInt(nts) then
+ p:=Factors(nts)[1];
+ e:=LogInt(nts,p);
+ pl:=[];
+ for j in [1..NrPerfectGroups(i)] do
+ q:=PerfectGroup(IsPermGroup,i,j);
+ new:=Name(q);
+ q:=Group(SmallGeneratingSet(q));
+ SetName(q,new);
+ Add(pl,q);
+ od;
+ for j in [1..Length(pl)] do
+ q:=pl[j];
+ #Print("Using ",i,", ",j,": ",q,"\n");
+ cf:=IrreducibleModules(q,GF(p),e)[2];
+ cf:=Filtered(cf,x->x.dimension=e);
+ for m in cf do
+ #Print("Module dimension ",m.dimension,"\n");
+ coh:=TwoCohomologyGeneric(q,m);
+
+ comp:=CompatiblePairs(q,m);
+ reps:=CompatiblePairOrbitRepsGeneric(comp,coh);
+ for v in reps do
+ new:=FpGroupCocycle(coh,v,true);
+ if IsPerfect(new) then
+ # could it have been gotten in another way?
+ pf:=Image(IsomorphismPermGroup(new));
+ nt:=NormalSubgroups(pf);
+ if ForAll(nt,x->Size(x)=1 or Size(x)>=nts) then
+ nt:=Filtered(nt,x->Size(x)=nts);
+ if (not ForAny(List(nt,x->pf/x),x->ForAny([1..j-1],y->
+ isot(pl[y],x)))) and ForAll(resp,
+ x->isot(x,Image(IsomorphismPermGroup(new)))=false) then
+ Add(res,new);
+ Add(resp,Image(IsomorphismPermGroup(new)));
+ #Print("found nr. ",Length(res),"\n");
+ else
+ #Print("smallerb\n");
+ fi;
+ #else Print("smallera\n");
+ fi;
+ fi;
+ od;
+
+ od;
+ od;
+ fi;
+ od;
+ return res;
+end;
+

tst/testextra/perfect.tst

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+#############################################################################
+##
+## Test for cohomology and isomorphism: Recompute perfect groups
+##
+gap> START_TEST("perfect.tst");
+gap> READ_GAP_ROOT("tst/testextra/makeperfect.g");;
+gap> l:=Practice(1920);;
+gap> Length(l);
+7
+gap> l:=Practice(10752);;
+gap> Length(l);
+9
+gap> STOP_TEST( "perfect.tst", 1);