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Homology of semigroups with 1‐6 elements

Dennis Sweeney edited this page Sep 26, 2024 · 10 revisions

Description

Below are some tables, listing out which semigroups have what homology.

The format is [H1, H2, H3, ...] : i1,i2,i3,...,ik:

  • Everything before the colon is a SageMath description of the homology, starting in degree 1, and going as far as I wanted to compute.
  • Everything after the colon is a comma-separated list of the ids in GAP's smallsemi package.

For example, the line [0, Z, 0, 0, 0] : 123 under 4-element semigroups below indicates that the semigroup SmallSemigroup(4, 123) in smallsemi has the homology of the 2-sphere. This can be computed using this repository as follows:

sage: op = op_from_id(4, 123)
sage: crs = find_best_gens_crs(op, 5)
sage: crs.homology_list(5)
[0, Z, 0, 0, 0]

One can also look up the ids by the row number in the text document here.

The data

Homology of 0-element semigroups
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] : (unnamed in smallsemi)
Homology of 1-element semigroups
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] : 1
Homology of 2-element semigroups
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] : 1,3,4
[C2, 0, C2, 0, C2, 0, C2, 0, C2, 0] : 2
Homology of 3-element semigroups
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] : 1,4,5,6,7,8,9,11,12,13,14,15,16,17
[C2, 0, C2, 0, C2, 0, C2, 0, C2, 0] : 2,3,10
[C3, 0, C3, 0, C3, 0, C3, 0, C3, 0] : 18
Homology of 4-element semigroups
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] : 1,2,3,8,9,10,11,14,15,16,17,18,19,20,21,22,23,24,25,29,33,34,35,36,38,39,40,41,42,43,44,45,46,47,48,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,91,92,93,94,95,96,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,124
[C2, 0, C2, 0, C2, 0, C2, 0, C2, 0] : 4,5,6,12,13,26,27,28,30,31,32,49,50,51,52,88,89,90
[C3, 0, C3, 0, C3, 0, C3, 0, C3, 0] : 97,125,126
[C4, 0, C4, 0, C4, 0, C4, 0, C4, 0] : 37
[C2 x C2, C2, C2 x C2 x C2, C2 x C2, C2 x C2 x C2 x C2, C2 x C2 x C2, C2^5, C2 x C2 x C2 x C2, C2^6, C2^5] : 7
[0, Z, 0, 0, 0, 0, 0, 0, 0, 0] : 123
Homology of 5-element semigroups
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] with zero element : 1,2,3,4,5,6,7,8,9,10,11,12,13,14,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,125,136,147,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,224,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,268,269,270,281,282,283,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,446,447,448,449,450,451,452,453,468,469,470,471,472,473,474,475,477,478,479,480,481,482,483,484,485,486,487,488,489,491,492,493,494,495,496,497,498,499,500,501,502,503,504,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,659,660,661,665,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1005,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1145,1146,1147,1148,1149,1153
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] : 1143
[C2, 0, C2, 0, C2, 0, C2, 0, C2, 0] : 15,16,17,18,19,20,21,22,23,25,57,58,59,60,61,62,63,64,65,66,115,116,117,118,119,120,121,122,123,124,126,127,128,129,130,131,132,133,134,135,137,138,139,140,141,142,143,144,145,146,178,179,180,181,182,183,184,222,223,225,226,259,260,261,262,263,264,265,266,267,271,272,273,274,275,276,277,278,279,280,284,285,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,454,455,456,457,458,459,460,461,462,463,464,465,466,467,518,653,654,655,656,657,658,662,663,664,666,667,668,669,956,957,958,959,960,961,962,963,964,965,1007
[C3, 0, C3, 0, C3, 0, C3, 0, C3, 0] : 476,540,1002,1003,1004,1006,1008,1009,1150,1151,1152,1154,1155,1156,1157,1158,1159
[C4, 0, C4, 0, C4, 0, C4, 0, C4, 0] : 185,186,490,505
[C2 x C2, C2, C2 x C2 x C2, C2 x C2, C2 x C2 x C2 x C2, C2 x C2 x C2, C2^5, C2 x C2 x C2 x C2, C2^6, C2^5] : 24,26,148
[0, Z, 0, 0, 0, 0, 0, 0, 0, 0] : 1142,1144
[0, Z, Z, Z, Z, Z, Z, Z, Z, Z] : 917
[C5, 0, C5, 0, C5, 0, C5, 0, C5, 0] : 1160
Homology of 6-element semigroups
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] with zero element : 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1264,1265,1266,1302,1358,1359,1360,1361,1362,1366,1398,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,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[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] : 14024,14079,14090,14150,14155,14551,14814,14817,15856,15858,15860,15862,15863,15865,15867,15869
[C2, 0, C2, 0, C2, 0, C2, 0, C2, 0] : 186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,235,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2583,2584,2846,2847,2848,2849,2850,2851,2852,2853,2854,2855,2856,2857,2858,2859,2860,2861,2862,2863,2868,2869,2870,2871,2872,2873,2874,2875,2877,2878,2879,2880,2881,2882,2884,2885,2886,2887,2888,2889,2890,2891,2892,2893,2894,2895,2896,2897,2898,2899,3063,3065,3067,3068,3069,3070,3071,3072,3073,3074,3075,3076,3077,3078,3079,3080,3081,3082,3083,3084,3085,3086,3087,3088,3089,3090,3091,3092,3093,3094,3095,3099,3100,3101,3102,3103,3104,3105,3106,3107,3108,3109,3110,3111,3112,3113,3114,3115,3116,3117,3118,3119,3120,3121,3122,3123,3124,3128,3129,3130,3131,3132,3133,3134,3135,3136,3137,3138,3139,3140,3141,3142,3143,3144,3145,3146,3147,3148,3149,3150,3151,3152,3153,3154,3155,3156,3157,3161,3162,3169,3170,4011,4012,4013,4014,4015,4016,4017,4018,4019,4020,4021,4022,4023,4024,4025,4026,4027,4028,4029,4030,4031,4032,4033,4034,4035,4036,4037,4038,4039,4040,4041,4042,4043,4044,4045,4046,4047,4048,4049,4050,4051,4052,4053,4054,4055,4056,4057,4058,4059,4060,4061,4062,4063,4064,4065,4066,4067,4068,4069,4070,4071,4072,4073,4074,4075,4076,4077,4078,4079,4080,4081,4082,4083,4084,4085,4086,4087,4088,4089,4090,4091,4092,4093,4094,4095,4096,4097,4098,4099,4100,4101,4102,4103,4119,4120,4121,4122,4123,4124,4125,4126,4127,4128,4129,4130,4131,4132,4133,4134,4135,4136,4137,4138,4139,4140,4141,4142,4143,4144,4145,4146,4147,4148,4149,4150,4151,4152,4153,4154,4155,4156,4157,4158,4159,4160,4161,4162,4163,4164,4165,4166,4167,4168,4169,4170,4171,4172,4173,4174,4175,4176,4177,4178,4179,4180,4181,4182,4183,4184,4185,4186,4187,4188,4189,4190,4191,4192,4193,4194,4195,4196,4197,4198,4199,4200,4201,4202,4203,4204,4205,4206,4207,4208,4209,4210,4226,4227,4228,4229,4230,4231,4232,4233,4234,4235,4236,4237,4238,4239,4240,4241,4242,4243,4244,4245,4246,4247,4248,4249,4250,4251,4252,4253,4254,4255,4256,4257,4258,4259,4260,4261,4262,4263,4264,4265,4266,4267,4268,4269,4270,4271,4272,4273,4274,4275,4276,4277,4278,4279,4280,4281,4282,4283,4284,4285,4286,4287,4288,4289,4290,4291,4292,4293,4294,4295,4296,4297,4298,4299,4300,4301,4302,4303,4304,4305,4306,4307,4308,4309,4832,4833,4834,4835,4836,4837,4838,4839,4840,4841,4842,4843,4844,4845,4846,4847,4848,4849,4850,4851,4852,4853,4854,4855,4856,4857,4858,4859,4860,4861,4862,4863,5299,5300,5301,5302,5303,5304,5305,5306,5310,5311,5313,5314,5315,5316,5317,5318,5319,5320,5482,5484,5486,5488,5489,5490,5491,5492,5493,5494,5495,5496,5500,5501,5502,5503,5504,5505,5506,5507,5511,5512,5734,5735,5736,5737,5738,5739,5740,5748,5749,5750,5751,5752,5753,5754,5820,5821,5822,5823,5824,5825,5826,5827,5828,5829,5830,5831,5832,5833,5834,5835,5836,5837,5838,5839,5840,5841,5842,5843,5844,5871,5872,5873,5878,5879,5880,6735,6736,6737,6738,6739,6743,6744,6745,6748,6749,6751,6754,6760,6765,6766,6767,6768,6769,6770,6771,6772,6773,6774,6775,6776,6777,6778,6779,6780,6781,6782,6783,6784,6785,6786,6787,6788,6789,6790,6791,6792,6793,6794,6795,6796,6797,6798,6799,6800,6801,6802,6803,6804,6805,6806,6807,6808,6809,6810,6811,6812,6813,6814,6815,6816,6817,6818,6819,6820,6821,6822,6823,6830,6831,6832,6833,6834,6835,6836,6837,6838,6839,6840,6841,6842,6843,6844,6845,6890,6891,6892,6893,6895,6896,6899,6900,6906,6912,6913,6914,6915,6916,6917,6918,6919,6920,6921,6922,6923,6924,6925,6926,6927,6928,6929,6930,6931,6932,6933,6934,6935,6936,6937,6938,6939,6940,6941,6942,6943,6944,6945,6946,6947,6948,6949,6950,6951,6952,6953,6954,6955,6956,6957,6958,6959,6960,6961,6962,6963,6964,6965,6966,6973,6974,6975,6976,6977,6978,6979,6980,6981,6982,6983,6984,6985,6986,6987,6988,7033,7034,7036,7037,7038,7039,7042,7043,7049,8799,8800,8801,8802,8803,8804,8805,8806,8807,8808,8809,8810,8811,8812,8813,8814,8815,8816,8817,8818,8819,8820,8821,8822,8823,8824,8825,8826,8827,8828,8829,8830,8831,8832,8833,8834,8835,8836,8837,8838,8839,8840,8841,8842,8843,8844,8845,8846,8847,8848,8849,8850,8851,8852,8853,8854,8855,8856,8857,8858,8859,8860,8861,8862,8863,8864,8865,8866,8867,8868,8869,8870,8871,8872,8873,8874,8875,8876,8877,8878,8879,8880,8881,8882,8883,8884,8949,8950,8951,8952,8953,8954,8955,8956,8957,8958,8959,8960,8961,8962,8963,8964,8965,8966,8967,8968,8969,8970,8971,8972,8973,8974,8975,8976,8977,8978,8979,8980,8981,8982,8983,8984,8985,8986,8987,8988,8989,8990,8991,8992,8993,8994,8995,8996,8997,8998,8999,9000,9001,9002,9003,9004,9005,9006,9007,9008,9009,9010,9011,9012,9013,9014,9015,9016,9017,9018,9019,9020,9021,9022,9023,9024,9025,9026,9112,9113,9114,9116,9117,9118,9395,9397,9399,9406,9407,9648,9649,9651,9654,9660,9949,9950,9951,9952,9953,9954,9955,9956,9957,9958,9959,9960,9961,9962,9963,9964,9965,9966,9967,9968,9969,9970,9971,9972,9973,9974,9975,9976,9977,9978,11758,11759,11760,11761,11762,11763,11764,11765,11766,11767,11768,11769,11770,11771,11772,11773,11774,11775,11776,11777,11778,11779,11780,11781,11782,11783,11784,11785,11786,11787,11788,11789,11790,11791,11792,11793,11794,11798,11800,11801,11802,11803,11805,11806,11809,11810,11811,11853,11854,11855,11856,11857,11858,11859,11860,11861,11862,11863,11864,11865,11866,11867,11868,11879,11880,11881,11882,11883,11884,11885,11886,11887,11888,11889,11890,11891,11892,11893,11894,11895,11896,11897,11936,14608,14609,14610,14611,14612,14613,14614,14615,14616,14617,14618,14619,14620,14621,14622,14623,14624,14625,14626,14627,14628,14629,14630,14631,14632,14633,14634,14635,14636,14637,14638,14639,14640,14641,14642,14643,14644,14645,14646,14647,14648,14649,14650,14651,14652,14653,14654,14960,14961,14962,14986
[C2 x C2, C2, C2 x C2 x C2, C2 x C2, C2 x C2 x C2 x C2, C2 x C2 x C2, C2^5, C2 x C2 x C2 x C2, C2^6, C2^5] : 213,234,236,237,960,961,1363,1364,1365,1399,1400,1401,3163,3164,3165,4325,4326,4327
[C4, 0, C4, 0, C4, 0, C4, 0, C4, 0] : 2302,2303,2304,4864,4865,5113,5114,5115,5324,5325,5326,5328,5329,5330,9265,9266,9335,9336,9337,9400,9401,9402,9496,9497,9498
[C3, 0, C3, 0, C3, 0, C3, 0, C3, 0] : 4334,4335,4336,5762,5763,5764,5765,9100,9101,9102,9103,9104,9105,9106,9107,9108,9109,9111,9115,9119,9120,9505,9506,9507,9802,9803,9805,9806,11930,11931,11932,11933,11934,11935,14927,14928,14929,14930,14931,14932,14933,14934,14935,14936,14937,14938,14939,14940,14941,14946,14948,14949,14951,14955,14959,14964,14966,14968,14972,14973,14974,14975,14976,14977,14978,14979,14980,14981,14983,14984,14985,14987,14988,14989,14990,14991,14992,14993,14994,14995,14997,14998,15904,15905,15906,15907,15908,15909,15910,15911,15912,15913,15921,15922,15923,15924,15925,15926,15927,15928,15929,15930,15931,15932,15933,15934,15936,15937,15938,15939,15940,15941,15942,15943,15944,15945,15947,15948,15949,15950,15951,15952,15953,15955,15956,15957,15958,15959,15962,15963,15964,15965,15966,15967,15968,15969,15970,15971,15972
[C2, 0, C6, 0, C2, 0, C6, 0, C2, 0] : 4337
[0, Z, Z x Z, Z x Z x Z x Z, Z^8, Z^16, Z^32, Z^64, Z^128, Z^256] : 8713,11726,11832
[0, Z, Z, Z, Z, Z, Z, Z, Z, Z] : 9766,14023,14089,14152,14333,14550
[0, Z, 0, 0, 0, 0, 0, 0, 0, 0] : 14052,14056,14080,14149,14154,14607,14813,15855,15857,15859,15861,15864,15866,15868,15871,15872,15873
[0, 0, Z, 0, 0, 0, 0, 0, 0, 0] : 14057,15870
[0, Z, C2, 0, C2, 0, C2, 0, C2, 0] : 14891,14897
[0, C2, 0, C2, 0, C2, 0, C2, 0, C2] : 14895
[C6, 0, C6, 0, C6, 0, C6, 0, C6, 0] : 14996
[C5, 0, C5, 0, C5, 0, C5, 0, C5, 0] : 14999,15961,15973
[0, Z x Z, 0, 0, 0, 0, 0, 0, 0, 0] : 15874
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