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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1486 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,425)(336,381,422)(339,384,419)(342,387,416)(345,390,413)(348,393,410)(351,396,407)(354,399,404)(357,402,401)(360,405,398)(363,408,395)(366,411,392)(369,414,389)(372,417,386)(375,420,383)(377,423,380)(379,427,477)(382,430,474)(385,433,471)(388,436,468)(391,439,465)(394,442,462)(397,445,459)(400,448,456)(403,451,453)(406,454,450)(409,457,447)(412,460,444)(415,463,441)(418,466,438)(421,469,435)(424,472,432)(426,475,429)(428,479,532)(431,482,529)(434,485,526)(437,488,523)(440,491,520)(443,494,517)(446,497,514)(449,500,511)(452,503,508)(455,506,505)(458,509,502)(461,512,499)(464,515,496)(467,518,493)(470,521,490)(473,524,487)(476,527,484)(478,530,481)(480,534,590)(483,537,587)(486,540,584)(489,543,581)(492,546,578)(495,549,575)(498,552,572)(501,555,569)(504,558,566)(507,561,563)(510,564,560)(513,567,557)(516,570,554)(519,573,551)(522,576,548)(525,579,545)(528,582,542)(531,585,539)(533,588,536)(535,592,651)(538,595,648)(541,598,645)(544,601,642)(547,604,639)(550,607,636)(553,610,633)(556,613,630)(559,616,627)(562,619,624)(565,622,621)(568,625,618)(571,628,615)(574,631,612)(577,634,609)(580,637,606)(583,640,603)(586,643,600)(589,646,597)(591,649,594)(593,653,715)(596,656,712)(599,659,709)(602,662,706)(605,665,703)(608,668,700)(611,671,697)(614,674,694)(617,677,691)(620,680,688)(623,683,685)(626,686,682)(629,689,679)(632,692,676)(635,695,673)(638,698,670)(641,701,667)(644,704,664)(647,707,661)(650,710,658)(652,713,655)(654,717,782)(657,720,779)(660,723,776)(663,726,773)(666,729,770)(669,732,767)(672,735,764)(675,738,761)(678,741,758)(681,744,755)(684,747,752)(687,750,749)(690,753,746)(693,756,743)(696,759,740)(699,762,737)(702,765,734)(705,768,731)(708,771,728)(711,774,725)(714,777,722)(716,780,719)(718,784,852)(721,787,849)(724,790,846)(727,793,843)(730,796,840)(733,799,837)(736,802,834)(739,805,831)(742,808,828)(745,811,825)(748,814,822)(751,817,819)(754,820,816)(757,823,813)(760,826,810)(763,829,807)(766,832,804)(769,835,801)(772,838,798)(775,841,795)(778,844,792)(781,847,789)(783,850,786)(785,854,925)(788,857,922)(791,860,919)(794,863,916)(797,866,913)(800,869,910)(803,872,907)(806,875,904)(809,878,901)(812,881,898)(815,884,895)(818,887,892)(821,890,889)(824,893,886)(827,896,883)(830,899,880)(833,902,877)(836,905,874)(839,908,871)(842,911,868)(845,914,865)(848,917,862)(851,920,859)(853,923,856)(855,927,1000)(858,930,997)(861,933,994)(864,936,991)(867,939,988)(870,942,985)(873,945,982)(876,948,979)(879,951,976)(882,954,973)(885,957,970)(888,960,967)(891,963,965)(894,928,962)(897,968,959)(900,971,956)(903,974,953)(906,977,950)(909,980,947)(912,983,944)(915,986,941)(918,989,938)(921,992,935)(924,995,932)(926,998,929)(931,1003,1072)(934,1006,1069)(937,1009,1066)(940,1012,1063)(943,1015,1060)(946,1018,1057)(949,1021,1054)(952,1024,1051)(955,1027,1048)(958,1030,1045)(961,1033,1042)(964,1036,1040)(966,1004,1038)(969,1041,1035)(972,1043,1032)(975,1046,1029)(978,1049,1026)(981,1052,1023)(984,1055,1020)(987,1058,1017)(990,1061,1014)(993,1064,1011)(996,1067,1008)(999,1070,1005)(1001,1073,1002)(1007,1076,1139)(1010,1079,1136)(1013,1082,1133)(1016,1085,1130)(1019,1088,1127)(1022,1091,1124)(1025,1094,1121)(1028,1097,1118)(1031,1100,1115)(1034,1103,1112)(1037,1106,1110)(1039,1077,1109)(1044,1111,1105)(1047,1113,1102)(1050,1116,1099)(1053,1119,1096)(1056,1122,1093)(1059,1125,1090)(1062,1128,1087)(1065,1131,1084)(1068,1134,1081)(1071,1137,1078)(1074,1140,1075)(1080,1143,1200)(1083,1146,1197)(1086,1149,1194)(1089,1152,1191)(1092,1155,1188)(1095,1158,1185)(1098,1161,1182)(1101,1164,1179)(1104,1167,1176)(1107,1170,1174)(1108,1144,1173)(1114,1175,1169)(1117,1177,1166)(1120,1180,1163)(1123,1183,1160)(1126,1186,1157)(1129,1189,1154)(1132,1192,1151)(1135,1195,1148)(1138,1198,1145)(1141,1201,1142)(1147,1204,1255)(1150,1207,1252)(1153,1210,1249)(1156,1213,1246)(1159,1216,1243)(1162,1219,1240)(1165,1222,1237)(1168,1225,1234)(1171,1228,1232)(1172,1205,1231)(1178,1233,1227)(1181,1235,1224)(1184,1238,1221)(1187,1241,1218)(1190,1244,1215)(1193,1247,1212)(1196,1250,1209)(1199,1253,1206)(1202,1256,1203)(1208,1259,1304)(1211,1262,1301)(1214,1265,1298)(1217,1268,1295)(1220,1271,1292)(1223,1274,1289)(1226,1277,1286)(1229,1280,1284)(1230,1260,1283)(1236,1285,1279)(1239,1287,1276)(1242,1290,1273)(1245,1293,1270)(1248,1296,1267)(1251,1299,1264)(1254,1302,1261)(1257,1305,1258)(1263,1308,1347)(1266,1311,1344)(1269,1314,1341)(1272,1317,1338)(1275,1320,1335)(1278,1323,1332)(1281,1326,1330)(1282,1309,1329)(1288,1331,1325)(1291,1333,1322)(1294,1336,1319)(1297,1339,1316)(1300,1342,1313)(1303,1345,1310)(1306,1348,1307)(1312,1351,1384)(1315,1354,1381)(1318,1357,1378)(1321,1360,1375)(1324,1363,1372)(1327,1366,1370)(1328,1352,1369)(1334,1371,1365)(1337,1373,1362)(1340,1376,1359)(1343,1379,1356)(1346,1382,1353)(1349,1385,1350)(1355,1388,1415)(1358,1391,1412)(1361,1394,1409)(1364,1397,1406)(1367,1400,1404)(1368,1389,1403)(1374,1405,1399)(1377,1407,1396)(1380,1410,1393)(1383,1413,1390)(1386,1416,1387)(1392,1419,1440)(1395,1422,1437)(1398,1425,1434)(1401,1428,1432)(1402,1420,1431)(1408,1433,1427)(1411,1435,1424)(1414,1438,1421)(1417,1441,1418)(1423,1444,1459)(1426,1447,1456)(1429,1450,1454)(1430,1445,1453)(1436,1455,1449)(1439,1457,1446)(1442,1460,1443)(1448,1463,1472)(1451,1466,1470)(1452,1464,1469)(1458,1471,1465)(1461,1473,1462)(1467,1476,1480)(1468,1477,1479)(1474,1481,1475)(1478,1482,1483);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,593,654,718,785,855,928,820,686,564,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,594,655,719,786,856,929,1002,1041,893,753,625,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,658,722,789,859,932,1005,1075,1111,968,823,689,567,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,661,725,792,862,935,1008,1078,1142,1175,1043,896,756,628,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,664,728,795,865,938,1011,1081,1145,1203,1233,1113,971,826,692,570,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,667,731,798,868,941,1014,1084,1148,1206,1258,1285,1177,1046,899,759,631,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,670,734,801,871,944,1017,1087,1151,1209,1261,1307,1331,1235,1116,974,829,695,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,737,804,874,947,1020,1090,1154,1212,1264,1310,1350,1371,1287,1180,1049,902,762,634,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,615,676,740,807,877,950,1023,1093,1157,1215,1267,1313,1353,1387,1405,1333,1238,1119,977,832,698,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,880,953,1026,1096,1160,1218,1270,1316,1356,1390,1418,1433,1373,1290,1183,1052,905,765,637,521,417,325,245,176,207,241,278,318,361,407,456,508,563,621,682,746,813,883,956,1029,1099,1163,1221,1273,1319,1359,1393,1421,1443,1455,1407,1336,1241,1122,980,835,701,579,469,371,285,210,244,281,321,364,410,459,511,566,624,685,749,816,886,959,1032,1102,1166,1224,1276,1322,1362,1396,1424,1446,1462,1471,1435,1376,1293,1186,1055,908,768,640,524,420,328,247,284,324,367,413,462,514,569,627,688,752,819,889,962,1035,1105,1169,1227,1279,1325,1365,1399,1427,1449,1465,1475,1481,1457,1410,1339,1244,1125,983,838,704,582,472,374,287,327,370,416,465,517,572,630,691,755,822,892,965,1038,927,1001,1074,1141,1202,1257,1306,1349,1386,1417,1442,1461,1474,1473,1438,1379,1296,1189,1058,911,771,643,527,423,330,373,419,468,520,575,633,694,758,825,895,967,1040,1109,1003,854,926,999,1071,1138,1199,1254,1303,1346,1383,1414,1439,1458,1460,1413,1342,1247,1128,986,841,707,585,475,376,422,471,523,578,636,697,761,828,898,970,1042,1110,1173,1076,930,784,853,924,996,1068,1135,1196,1251,1300,1343,1380,1411,1436,1441,1382,1299,1192,1061,914,774,646,530,425,474,526,581,639,700,764,831,901,973,1045,1112,1174,1231,1143,1006,857,717,783,851,921,993,1065,1132,1193,1248,1297,1340,1377,1408,1416,1345,1250,1131,989,844,710,588,477,529,584,642,703,767,834,904,976,1048,1115,1176,1232,1283,1204,1079,933,787,653,716,781,848,918,990,1062,1129,1190,1245,1294,1337,1374,1385,1302,1195,1064,917,777,649,532,587,645,706,770,837,907,979,1051,1118,1179,1234,1284,1329,1259,1146,1009,860,720,592,652,714,778,845,915,987,1059,1126,1187,1242,1291,1334,1348,1253,1134,992,847,713,590,648,709,773,840,910,982,1054,1121,1182,1237,1286,1330,1369,1308,1207,1082,936,790,656,534,591,650,711,775,842,912,984,1056,1123,1184,1239,1288,1305,1198,1067,920,780,651,712,776,843,913,985,1057,1124,1185,1240,1289,1332,1370,1403,1351,1262,1149,1012,863,723,595,479,533,589,647,708,772,839,909,981,1053,1120,1181,1236,1256,1137,995,850,715,779,846,916,988,1060,1127,1188,1243,1292,1335,1372,1404,1431,1388,1311,1210,1085,939,793,659,537,427,478,531,586,644,705,769,836,906,978,1050,1117,1178,1201,1070,923,782,849,919,991,1063,1130,1191,1246,1295,1338,1375,1406,1432,1453,1419,1354,1265,1152,1015,866,726,598,482,378,426,476,528,583,641,702,766,833,903,975,1047,1114,1140,998,852,922,994,1066,1133,1194,1249,1298,1341,1378,1409,1434,1454,1469,1444,1391,1314,1213,1088,942,796,662,540,430,332,377,424,473,525,580,638,699,763,830,900,972,1044,1073,925,997,1069,1136,1197,1252,1301,1344,1381,1412,1437,1456,1470,1479,1463,1422,1357,1268,1155,1018,869,729,601,485,381,289,331,375,421,470,522,577,635,696,760,827,897,969,1000,1072,1139,1200,1255,1304,1347,1384,1415,1440,1459,1472,1480,1483,1476,1447,1394,1317,1216,1091,945,799,665,543,433,335,249,288,329,372,418,467,519,574,632,693,757,824,894,966,1039,1108,1172,1230,1282,1328,1368,1402,1430,1452,1468,1478,1482,1466,1425,1360,1271,1158,1021,872,732,604,488,384,292,212,248,286,326,369,415,464,516,571,629,690,754,821,891,964,1037,1107,1171,1229,1281,1327,1367,1401,1429,1451,1467,1477,1450,1397,1320,1219,1094,948,802,668,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,687,751,818,888,961,1034,1104,1168,1226,1278,1324,1364,1398,1426,1448,1464,1428,1363,1274,1161,1024,875,735,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,684,748,815,885,958,1031,1101,1165,1223,1275,1321,1361,1395,1423,1445,1400,1323,1222,1097,951,805,671,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,620,681,745,812,882,955,1028,1098,1162,1220,1272,1318,1358,1392,1420,1366,1277,1164,1027,878,738,610,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,617,678,742,809,879,952,1025,1095,1159,1217,1269,1315,1355,1389,1326,1225,1100,954,808,674,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,806,876,949,1022,1092,1156,1214,1266,1312,1352,1280,1167,1030,881,741,613,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,803,873,946,1019,1089,1153,1211,1263,1309,1228,1103,957,811,677,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,870,943,1016,1086,1150,1208,1260,1170,1033,884,744,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,867,940,1013,1083,1147,1205,1106,960,814,680,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,794,864,937,1010,1080,1144,1036,887,747,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,861,934,1007,1077,963,817,683,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,858,931,1004,890,750,622,506,402,310,230,162,106,62,30,10)(1484,1485,1486)
Conjugacy classes & character table
1491 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13347, 3);
Finite Group Databasebeta