Conway Groups

Author

Eric W. Weisstein
November 11, 2010

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GroupTheory/ConwayGroups.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ConwayGroups.html.

©2010 Wolfram Research, Inc. except for portions noted otherwise

Order

m=Symbol/@Names["ConwayGroup*"]

Grid[{
#,
Transitivity[#[]],
p=PermutationSupport[#[]];If[ListQ[p],Length[p],$Failed],
g=GroupOrder[#[]],
Times@@Superscript@@@FactorInteger[g]
}&/@m,Alignment->{{Left,Decimal,Decimal,Decimal,Left},Automatic},Dividers->All]//TraditionalForm

Permutation Representations

(Subscript[Co, 1])

degree 98280

p={{2,1,5,7,3,10,4,12,13,6,16,8,9,20,21,11,24,25,27,14,15,31,32,17,18,36,19,38,39,41,22,23,45,46,48,26,51,28,29,55,30,57,58,60,33,34,64,35,66,67,37,70,71,73,40,76,42,43,80,44,82,83,85,47,88,49,50,92,93,52,53,97,54,99,100,56,103,104,106,59,109,61,62,113,63,115,116,65,119,120,122,68,69,126,127,129,72,132,74,75,136,137,77,78,141,79,143,144,81,147,148,150,84,153,86,87,157,158,89,90,162,91,164,165,167,94,95,171,96,173,174,98,177,178,180,101,102,184,185,187,105,190,107,108,194,195,110,111,199,112,201,202,114,205,206,208,117,118,212,213,215,121,218,123,124,222,125,224,225,227,128,230,130,131,234,235,133,134,239,135,241,242,244,138,139,248,140,250,251,142,254,255,257,145,146,261,262,264,149,267,151,152,271,272,154,155,276,156,278,279,281,159,160,285,161,287,288,163,291,292,294,166,297,168,169,301,170,302,243,172,305,306,308,175,176,312,313,315,179,318,181,182,229,183,323,324,326,186,329,188,189,333,334,191,192,338,193,340,341,343,196,197,347,198,349,350,200,353,354,356,203,204,360,361,363,207,366,209,210,370,211,372,373,375,214,378,216,217,382,383,219,220,387,221,389,390,223,393,394,395,226,228,399,400,231,232,404,233,406,407,409,236,237,413,238,364,415,240,418,419,421,423,245,246,427,247,429,430,249,433,380,435,252,253,439,440,442,256,445,258,259,449,260,451,452,454,263,457,265,266,461,462,268,269,466,270,468,469,471,273,274,475,275,316,477,277,480,481,483,280,486,282,283,490,284,492,493,286,496,331,498,289,290,502,503,505,293,508,295,296,512,513,298,299,300,518,519,520,303,304,524,525,527,307,530,309,310,534,311,536,537,539,314,542,317,545,546,319,320,550,321,552,322,554,555,557,325,560,327,328,564,565,330,568,332,570,571,573,335,336,577,337,528,579,339,582,583,585,342,588,344,345,591,346,593,594,348,597,598,600,351,352,604,605,607,355,610,357,358,614,359,616,617,619,362,622,365,625,626,367,368,630,369,632,633,371,636,637,639,374,642,376,377,646,647,379,650,381,652,653,655,384,385,659,386,608,661,388,664,665,667,391,392,671,672,674,676,396,397,398,681,682,684,401,402,688,403,443,690,405,693,694,696,408,699,410,411,703,412,705,706,414,709,710,416,417,714,715,717,420,720,422,723,424,425,727,426,729,730,428,733,734,736,431,432,740,741,434,744,436,437,748,438,750,751,753,441,756,444,759,760,446,447,764,448,766,767,450,770,771,453,774,455,456,778,779,458,459,783,460,785,786,788,463,464,792,465,506,794,467,797,798,800,470,803,472,473,807,474,809,810,476,813,814,478,479,818,819,821,482,824,484,485,828,829,487,488,833,489,835,836,491,839,840,842,494,495,846,847,497,850,499,500,854,501,856,857,859,504,862,507,865,866,509,510,870,511,872,873,875,514,515,879,516,881,517,883,884,886,796,521,522,891,523,893,894,896,526,899,529,902,903,531,532,907,533,909,910,535,913,914,916,538,919,540,541,923,924,543,544,928,929,931,547,548,935,549,888,937,551,940,941,553,944,945,947,556,950,558,559,954,955,561,562,959,563,961,962,964,566,567,968,969,569,972,973,975,572,978,574,575,982,576,984,985,578,988,989,580,581,993,994,996,584,999,586,587,1003,1004,589,590,1008,1009,592,1012,1013,1015,595,596,1019,1020,1022,599,1025,601,602,1029,603,1031,1032,1034,606,1037,609,1040,680,611,612,1044,613,1046,1047,615,1050,1051,1053,618,1056,620,621,1060,1061,623,624,1065,1066,1068,627,628,1072,629,1023,1074,631,1077,1078,1080,634,635,1084,1085,1087,638,1090,640,641,1094,1095,643,644,1099,645,1101,1102,1104,648,649,1108,1109,651,1112,1113,1115,654,1118,656,657,1122,658,1124,1125,660,1128,1129,662,663,1133,1134,1136,666,1139,668,669,1143,670,1145,1146,1148,673,1151,675,1154,677,678,1158,679,1160,718,1161,1163,683,1166,685,686,1170,687,1172,1173,689,1176,1177,691,692,1181,1182,1184,695,1187,697,698,1191,1192,700,701,1196,702,1198,1199,704,1202,1203,1205,707,708,1209,1210,1212,711,712,1216,713,1218,1219,1221,716,1224,719,1227,1228,721,722,1232,1233,724,725,1237,726,1239,1240,728,1243,1244,1246,731,732,1250,1251,1253,735,1256,737,738,1260,739,1262,1263,1265,742,743,1269,1270,745,746,1274,747,1276,1277,749,1280,1281,1283,752,1286,754,755,1290,1291,757,758,1295,1296,1298,761,762,1302,763,1254,1304,765,1307,1308,1310,768,769,1314,1315,1317,772,773,1321,1322,775,776,1326,777,1328,1329,1331,780,781,1335,782,822,1337,784,1340,1341,1343,787,1346,789,790,1350,791,1352,1353,793,1356,1357,795,1360,1361,1363,799,1366,801,802,1370,1371,804,805,1375,806,1377,1378,808,1381,1382,1384,811,812,1388,1389,1391,815,816,1395,817,1397,1398,1400,820,1403,823,1406,1407,825,826,1411,827,1413,1414,1416,830,831,1420,832,1422,1423,834,1426,1427,1429,837,838,1433,1434,1436,841,1439,843,844,1443,845,1445,1446,1448,848,849,1452,1453,851,852,1457,853,1459,1460,855,1463,1464,1466,858,1469,860,861,1473,1474,863,864,1478,1479,1481,867,868,1485,869,1437,1487,871,1490,1491,1493,874,1496,876,877,1500,878,1502,1503,880,1506,1230,882,1509,1510,1512,885,1515,887,889,1519,890,1521,1522,892,1525,1526,1528,895,1531,897,898,1535,1536,900,901,1540,1541,1543,904,905,1547,906,1513,1549,908,1552,1553,1555,911,912,1559,1560,1562,915,1565,917,918,1569,1570,920,921,1574,922,1576,1577,1579,925,926,1583,927,158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98107,97308,97127,94678,96332,96274,94692,97691,94700,98002,98127,98136,98202,97273,94763,98203,96739,97856,97136,94752,98206,96766,98208,97626,98034,94774,98172,98100,98210,98211,97898,97119,98212,97868,94818,98143,97075,94831,96469,98215,96999,98216,95911,96903,97923,98218,96424,97978,97429,96647,96264,94935,95682,94948,95587,97360,98219,97596,94976,98080,95489,97924,98221,97124,95031,96960,97345,95046,98201,98223,97767,98099,98161,98092,96080,95123,95411,96597,97726,97786,97815,95187,95191,98144,98224,95205,98225,98118,96713,98226,98227,95282,95661,98228,97331,95300,98220,98108,97935,97219,95321,97236,98230,97569,97240,98231,98129,96268,95388,96406,96408,96596,98232,97903,97836,98066,95435,95441,98016,95450,95829,96761,95468,95979,97353,96872,98089,95817,98046,98238,95516,95709,98239,96534,96500,97710,97934,97139,97555,97557,97541,96948,96975,95654,98240,95659,97531,96784,97970,97882,96876,98241,96868,97690,96439,95987,98197,97529,97118,95766,98138,96920,98242,96208,95906,98200,98198,97351,95830,98182,97908,98217,95837,98207,95852,97161,97253,97165,97024,96435,95903,98235,98068,98179,98062,96962,97270,96397,95978,98199,98152,98000,96020,98244,96502,96039,97224,96059,96466,97035,97009,96117,96937,98248,97304,96977,98149,97524,98249,96173,96374,98234,96194,98251,98252,96680,97476,98253,96242,97389,97992,97041,98254,97177,96282,96333,96354,97869,97363,97425,98256,98153,97805,96444,97817,98246,98236,98051,96524,98186,98259,96548,96557,98261,96582,97584,96610,98262,98154,96639,97022,98156,97388,98073,98264,98265,98266,97536,98103,97342,97498,98035,98257,96783,97994,97464,96805,96810,97057,98071,98192,97358,96853,96896,97486,97463,97905,97571,98204,98237,98058,96988,98087,98267,97006,97502,97014,98125,97859,98268,98269,98270,98139,97914,97466,98260,97082,97969,97269,97183,98271,97158,97216,98263,97233,97243,97848,98272,97285,97293,97946,98273,97650,98180,97757,97990,98159,97368,98037,98175,97484,98275,98250,98229,97753,98169,98209,97644,98115,97742,97933,98214,98005,98162,98112,97864,98213,98255,98093,97785,98247,98008,97832,97847,98278,98277,97951,97954,98258,98280,98245,98279,98274,98276,98243,98205,98178,98233,98222}};

Compute

Dimensions[p]

co1=PermutationGroup[System`Cycles/@List/@p];

$Version

GroupOrder[co1]//Timing

runs byblis66 out of memory

Messages

GroupOrbits[ConwayGroupCo1[],blah]

GroupOrbits[co1=ConwayGroupCo1[],PermutationSupport[co1]]