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Aliases
Splittings
Subgroups
27 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1372 points:
(2,4,9)(3,7,17)(5,12,29)(6,15,37)(8,20,49)(10,24,22)(11,27,42)(13,32,73)(14,35,81)(16,40,93)(18,44,23)(19,47,43)(21,52,118)(25,57,66)(26,60,86)(28,64,111)(30,68,53)(31,71,98)(33,76,159)(34,79,166)(36,84,177)(38,88,54)(39,91,99)(41,96,201)(45,103,67)(46,106,87)(48,109,112)(50,113,55)(51,116,100)(56,62,101)(58,126,153)(59,129,170)(61,132,194)(63,108,102)(65,139,239)(69,144,140)(70,147,182)(72,151,226)(74,155,120)(75,127,206)(77,161,302)(78,164,308)(80,168,316)(82,172,121)(83,175,207)(85,180,339)(89,186,141)(90,189,183)(92,192,227)(94,196,122)(95,199,208)(97,204,123)(104,215,154)(105,218,171)(107,221,195)(110,225,240)(114,231,142)(115,234,184)(117,237,228)(119,241,209)(124,137,229)(125,149,210)(128,252,312)(130,255,332)(131,191,211)(133,259,371)(134,213,143)(135,220,185)(136,224,230)(138,236,212)(145,275,289)(146,278,320)(148,281,359)(150,223,214)(152,288,427)(156,293,269)(157,276,344)(158,297,407)(160,300,243)(162,303,505)(163,306,511)(165,310,517)(167,314,244)(169,318,530)(173,324,270)(174,327,345)(176,330,408)(178,334,245)(179,337,382)(181,342,272)(187,350,290)(188,352,321)(190,354,360)(193,358,428)(197,363,271)(198,366,346)(200,369,409)(202,373,246)(203,376,383)(205,380,347)(216,393,299)(217,396,313)(219,399,333)(222,403,372)(232,416,291)(233,419,322)(235,422,361)(238,426,429)(242,431,410)(247,267,378)(248,286,411)(249,250,384)(251,404,392)(253,441,526)(254,329,385)(256,445,560)(257,357,412)(258,368,386)(260,391,292)(261,398,323)(262,402,362)(263,406,379)(264,414,273)(265,421,348)(266,425,413)(268,430,387)(274,283,388)(277,468,520)(279,471,548)(280,356,389)(282,475,599)(284,401,349)(285,405,415)(287,424,390)(294,491,485)(295,492,533)(296,495,584)(298,499,669)(301,502,460)(304,506,750)(305,509,755)(307,512,759)(309,515,433)(311,488,319)(315,524,461)(317,528,434)(325,539,486)(326,541,534)(328,543,585)(331,547,670)(335,552,462)(336,555,571)(338,558,644)(340,562,435)(341,565,617)(343,569,536)(351,576,521)(353,578,549)(355,580,600)(364,590,487)(365,592,535)(367,594,586)(370,598,671)(374,603,463)(375,606,572)(377,609,645)(381,615,587)(394,628,504)(395,631,514)(397,634,527)(400,638,561)(417,655,500)(418,658,522)(420,661,550)(423,665,601)(432,675,672)(436,483,611)(437,497,646)(438,620,466)(439,639,575)(440,642,654)(442,683,782)(443,546,647)(444,557,618)(446,583,612)(447,597,648)(448,608,619)(449,627,501)(450,633,523)(451,637,551)(452,641,602)(453,653,489)(454,660,537)(455,664,588)(456,668,613)(457,567,464)(458,614,573)(459,674,649)(465,480,650)(467,581,625)(469,706,776)(470,545,621)(472,710,816)(473,582,651)(474,596,622)(476,624,490)(477,636,538)(478,640,589)(479,643,568)(481,663,574)(482,667,652)(484,673,623)(493,733,769)(494,735,801)(496,738,855)(498,666,626)(503,747,725)(507,751,993)(508,753,996)(510,756,1000)(513,729,696)(516,763,700)(518,766,676)(519,682,744)(525,775,726)(529,780,701)(531,784,677)(532,786,772)(540,793,770)(542,795,802)(544,797,856)(553,807,727)(554,809,788)(556,811,842)(559,815,927)(563,820,702)(564,823,834)(566,826,900)(570,832,804)(577,837,777)(579,839,817)(591,847,771)(593,849,803)(595,851,857)(604,861,728)(605,863,789)(607,865,843)(610,869,928)(616,876,858)(629,885,749)(630,888,758)(632,891,765)(635,894,783)(656,911,748)(657,914,761)(659,917,778)(662,921,818)(678,742,870)(679,880,731)(680,895,792)(681,898,846)(684,800,871)(685,814,901)(686,825,877)(687,854,872)(688,868,902)(689,890,762)(690,893,779)(691,897,819)(692,910,745)(693,916,773)(694,920,805)(695,924,859)(697,831,790)(698,875,844)(699,931,873)(703,722,828)(704,739,903)(705,840,908)(707,952,1026)(708,799,904)(709,813,878)(711,841,829)(712,853,905)(713,867,879)(714,884,746)(715,892,774)(716,896,806)(717,899,860)(718,907,730)(719,919,791)(720,923,845)(721,926,830)(723,874,835)(724,930,906)(732,798,881)(734,975,1019)(736,977,1055)(737,852,882)(740,922,836)(741,925,909)(743,929,883)(752,994,1187)(754,997,1190)(757,972,965)(760,951,990)(764,1008,969)(767,1011,948)(768,983,1005)(781,1025,970)(785,1030,949)(787,1033,1022)(794,1038,1020)(796,1040,1056)(808,1048,1014)(810,1050,1043)(812,1052,1087)(821,1061,971)(822,1063,1035)(824,1065,1079)(827,1069,1143)(833,1076,1058)(838,1078,1027)(848,1082,1021)(850,1084,1057)(862,1091,1015)(864,1093,1044)(866,1095,1088)(886,1107,992)(887,1110,999)(889,1112,1003)(912,1128,991)(913,1131,1002)(915,1134,1009)(918,1137,1028)(932,1106,989)(933,1115,1018)(934,1118,1047)(935,987,944)(936,1054,1099)(937,1068,1120)(938,1098,1100)(939,1114,1010)(940,1117,1029)(941,1133,1006)(942,1136,1023)(943,1140,1059)(945,1032,1016)(946,1075,1045)(947,1103,1089)(950,984,1070)(953,1042,1071)(954,1053,1121)(955,1067,1104)(956,1086,1072)(957,1097,1122)(958,1113,1007)(959,1116,1024)(960,1119,1060)(961,1127,988)(962,1135,1017)(963,1139,1046)(964,1142,1090)(966,1074,1036)(967,1102,1080)(968,1145,1073)(973,980,1123)(974,1041,1124)(976,1171,1213)(978,1085,1125)(979,1096,1105)(981,1138,1037)(982,1141,1081)(985,1101,1077)(986,1144,1126)(995,1188,1194)(998,1169,1178)(1001,1170,1184)(1004,1172,1195)(1012,1191,1167)(1013,1181,1201)(1031,1219,1168)(1034,1204,1216)(1039,1223,1214)(1049,1227,1208)(1051,1229,1231)(1062,1235,1205)(1064,1237,1224)(1066,1239,1250)(1083,1249,1215)(1092,1252,1209)(1094,1254,1232)(1108,1240,1186)(1109,1261,1189)(1111,1263,1193)(1129,1271,1185)(1130,1273,1192)(1132,1275,1196)(1146,1264,1200)(1147,1266,1212)(1148,1182,1163)(1149,1242,1257)(1150,1277,1202)(1151,1280,1217)(1152,1177,1198)(1153,1221,1210)(1154,1247,1233)(1155,1230,1243)(1156,1241,1268)(1157,1256,1244)(1158,1265,1203)(1159,1267,1218)(1160,1276,1199)(1161,1279,1211)(1162,1282,1234)(1164,1220,1206)(1165,1246,1225)(1166,1259,1251)(1173,1255,1269)(1174,1270,1183)(1175,1278,1207)(1176,1281,1226)(1179,1245,1222)(1180,1258,1248)(1197,1293,1308)(1228,1325,1318)(1236,1328,1315)(1238,1330,1326)(1253,1336,1319)(1260,1331,1302)(1262,1338,1304)(1272,1340,1303)(1274,1342,1306)(1283,1339,1305)(1284,1301,1297)(1285,1300,1312)(1286,1309,1320)(1287,1332,1333)(1288,1344,1313)(1289,1346,1321)(1290,1296,1310)(1291,1323,1316)(1292,1335,1327)(1294,1343,1311)(1295,1345,1317)(1298,1322,1314)(1299,1334,1324)(1307,1337,1356)(1329,1364,1361)(1341,1365,1354)(1347,1353,1359)(1348,1357,1362)(1349,1366,1355)(1350,1358,1351)(1352,1363,1360)(1367,1368,1369)(1371,1372);(1,668,207,925,626,633,1302,880,1316,172,869,360,1097,1003,847,1073,414,1238,1011,1293,561,964,966,1159,1160,603,200,202,353,364,440,497,727,679,1169,470,580,3,224,382,404,883,74,1346,747,1263,323,369,586,596,1196,350,1076,651,1246,1203,1131,818,825,1165,1055,1288,860,370,375,579,591,682,740,971,933,1171,708,132,8,18,617,13,894,157,1116,989,509,537,91,843,182,1308,575,661,905,919,1313,628,1058,332,1292,1000,1328,1090,380,607,611,848,530,982,984,1147,1174,953,258,21,46,643,34,168,296,315,1183,492,790,9,854,345,1085,836,218,1122,388,1359,314,1069,549,1241,1193,1048,1251,113,866,871,1083,783,1177,1179,1284,1294,820,447,52,107,114,80,216,496,162,1301,732,797,23,357,571,581,1077,12,1140,621,1281,523,558,803,813,1306,539,1254,230,875,1099,1101,1028,910,1299,1213,1349,1060,687,119,222,233,169,395,531,305,781,974,281,55,62,834,120,1078,31,637,878,895,773,175,1044,320,1356,792,849,413,421,1257,646,1216,526,1353,1190,1340,1234,606,242,239,420,319,632,656,510,886,1170,474,123,135,841,244,441,72,82,1104,145,1016,29,1054,534,994,1037,352,649,101,1259,515,1134,777,1276,1304,1107,1327,196,432,428,662,532,786,913,757,1109,1030,712,139,262,264,434,449,152,174,1119,277,512,67,546,788,798,1222,57,665,211,923,762,631,1021,884,1354,775,1330,362,431,671,673,787,416,1132,1001,1262,1218,956,268,452,454,677,689,180,328,335,469,495,142,149,1035,269,1223,125,221,386,401,1006,76,1209,520,1366,1018,1050,588,116,928,226,1034,654,1221,1194,1322,1321,823,459,371,694,696,939,341,544,554,707,737,272,284,1042,461,706,248,15,619,25,1198,73,1114,770,1264,1207,541,844,17,931,408,1144,909,916,1307,1123,1362,334,699,600,943,945,1091,566,567,810,821,978,288,478,480,701,714,436,39,641,59,898,154,309,1014,503,1314,144,851,43,425,644,666,1126,391,1357,1008,1342,551,609,857,867,1153,590,827,829,1051,1062,1172,484,717,719,949,958,445,92,94,130,187,291,250,1205,485,997,274,354,100,108,900,206,1137,625,1279,1200,1110,805,199,1088,359,1286,846,832,1072,1074,1236,911,724,560,963,965,1158,686,193,198,256,351,488,439,767,726,975,465,60,209,2,926,159,634,882,892,1311,303,1045,37,1098,585,1255,1081,419,1244,650,1329,528,968,817,1162,1164,1235,937,204,367,374,577,499,681,739,970,932,703,131,225,6,405,299,79,1105,156,1358,293,1052,87,597,842,852,1248,103,1247,904,1334,779,826,1057,1067,1291,807,1149,379,595,605,838,743,935,981,1168,1146,710,257,20,16,45,500,33,1117,295,1266,490,543,184,191,1079,344,1249,214,920,1121,1138,1023,337,1232,548,1348,1047,1093,613,614,864,870,986,782,1176,1178,1283,955,446,51,41,105,744,78,317,494,525,730,147,347,22,1086,302,837,390,398,1268,620,1210,81,1242,802,1331,1226,592,873,229,1094,766,1181,1027,1296,1298,1271,1156,373,117,97,219,232,165,394,736,304,972,280,358,54,582,504,252,623,30,1282,502,1112,171,814,1043,751,1324,186,876,412,1102,1010,914,1215,1127,1352,1025,1287,602,238,205,400,418,311,630,785,508,977,473,64,122,134,748,243,638,70,896,746,306,322,329,1224,533,1325,349,422,648,663,1202,393,1319,776,1368,1212,1237,859,241,381,427,659,519,889,912,754,1108,711,138,246,261,990,433,84,148,173,988,276,536,66,1230,505,1038,574,106,902,210,1312,166,1277,1020,1343,1317,809,1089,49,616,670,918,768,1032,1130,998,1260,562,266,267,451,453,676,179,282,326,1182,467,547,141,799,749,468,835,4,924,385,1141,313,890,1208,1106,1360,324,1095,112,674,927,929,1013,653,1274,1191,1337,819,456,458,691,693,861,338,340,542,553,705,151,271,283,991,460,839,11,402,618,639,522,160,1315,769,1338,538,594,228,236,1143,407,1204,908,1323,1305,1273,1059,376,698,599,942,944,559,564,796,808,951,287,463,477,1184,700,255,28,38,877,58,772,153,1265,750,753,791,189,410,42,1145,308,917,1125,1135,1355,885,1233,93,947,856,1151,1152,569,824,828,1049,784,482,483,716,718,948,444,65,90,899,128,310,290,516,992,733,1036,24,426,99,667,514,396,1269,624,1369,524,1239,195,868,1087,1096,1285,231,1066,1071,1228,1029,721,723,960,962,1061,685,96,190,197,253,297,487,438,1185,725,1040,56,109,208,223,761,32,1280,881,1345,774,811,361,368,1250,584,1336,415,1075,1243,1245,1217,565,967,816,1161,1163,936,203,355,365,442,498,728,680,1012,969,471,124,7,383,5,1005,75,893,993,1115,1017,327,587,86,1256,511,1082,652,660,1333,903,1320,177,1166,1056,1289,1290,863,377,378,593,604,741,742,934,980,1167,709,247,19,406,14,642,158,167,1186,294,1206,68,598,183,853,758,576,906,213,1335,763,1275,333,1068,1231,1240,1347,363,610,612,850,862,983,985,1148,1175,1219,954,259,48,50,36,104,298,77,1267,493,756,143,192,346,356,1002,126,921,389,1139,1007,888,550,557,1326,801,1364,589,615,872,874,1092,655,1180,1026,1295,1297,1155,448,110,115,85,217,318,163,529,734,735,273,27,572,53,1195,249,399,622,636,1199,161,804,170,1332,755,1227,845,234,1100,411,1253,316,1300,1214,1350,1351,1063,688,118,235,181,397,417,307,629,976,507,464,63,583,121,840,437,35,879,69,1310,155,815,321,1053,999,793,1080,44,1103,647,1258,527,1133,1318,1270,1367,552,938,240,423,343,635,657,513,887,1031,752,475,136,137,245,260,678,83,897,146,1118,292,330,535,545,1192,275,1084,102,664,901,922,778,627,1361,1019,1365,806,865,429,430,570,669,915,760,1111,1129,995,713,263,265,435,450,683,176,178,279,325,489,71,789,140,1188,466,578,212,220,1120,384,1022,312,1344,996,1261,1046,366,672,111,833,517,1033,1004,1220,1272,1128,957,201,455,457,690,692,331,336,472,540,729,150,800,270,1041,704,129,387,10,1142,300,891,521,1113,1189,506,1225,88,675,227,930,765,658,1197,907,1341,780,1157,372,695,697,940,941,342,556,563,794,738,285,286,462,476,950,254,403,26,640,501,164,771,301,1303,491,1229,185,237,409,424,1009,215,1309,1124,1363,1024,1065,601,608,946,855,1150,568,812,822,1039,979,479,481,702,715,952,443,40,61,89,745,127,1015,289,1339,731,795,348,47,645,98,1201,392,1136,1187,1278,1211,555,858,194,1154,759,1252,830,831,1064,1070,1173,339,720,722,959,961,684,95,133,188,987,251,518,486,764,973,278,573)(1370,1371,1372)
Conjugacy classes & character table
1377 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 11);
Finite Group Databasebeta