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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1660 points:
(2,3)(5,6,8)(7,10,15)(9,13,12)(11,17,25)(14,20,22)(16,23,19)(18,27,38)(21,30,35)(24,33,32)(26,36,29)(28,40,54)(31,43,51)(34,46,48)(37,49,45)(39,52,42)(41,56,73)(44,59,70)(47,62,67)(50,65,64)(53,68,61)(55,71,58)(57,75,95)(60,78,92)(63,81,89)(66,84,86)(69,87,83)(72,90,80)(74,93,77)(76,97,120)(79,100,117)(82,103,114)(85,106,111)(88,109,108)(91,112,105)(94,115,102)(96,118,99)(98,122,148)(101,125,145)(104,128,142)(107,131,139)(110,134,136)(113,137,133)(116,140,130)(119,143,127)(121,146,124)(123,150,179)(126,153,176)(129,156,173)(132,159,170)(135,162,167)(138,165,164)(141,168,161)(144,171,158)(147,174,155)(149,177,152)(151,181,213)(154,184,210)(157,187,207)(160,190,204)(163,193,201)(166,196,198)(169,199,195)(172,202,192)(175,205,189)(178,208,186)(180,211,183)(182,215,250)(185,218,247)(188,221,244)(191,224,241)(194,227,238)(197,230,235)(200,233,232)(203,236,229)(206,239,226)(209,242,223)(212,245,220)(214,248,217)(216,252,290)(219,255,287)(222,258,284)(225,261,281)(228,264,278)(231,267,275)(234,270,272)(237,273,269)(240,276,266)(243,279,263)(246,282,260)(249,285,257)(251,288,254)(253,292,333)(256,295,330)(259,298,327)(262,301,324)(265,304,321)(268,307,318)(271,310,315)(274,313,312)(277,316,309)(280,319,306)(283,322,303)(286,325,300)(289,328,297)(291,331,294)(293,335,379)(296,338,376)(299,341,373)(302,344,370)(305,347,367)(308,350,364)(311,353,361)(314,356,358)(317,359,355)(320,362,352)(323,365,349)(326,368,346)(329,371,343)(332,374,340)(334,377,337)(336,381,428)(339,384,425)(342,387,422)(345,390,419)(348,393,416)(351,396,413)(354,399,410)(357,402,407)(360,405,404)(363,408,401)(366,411,398)(369,414,395)(372,417,392)(375,420,389)(378,423,386)(380,426,383)(382,430,480)(385,433,477)(388,436,474)(391,439,471)(394,442,468)(397,445,465)(400,448,462)(403,451,459)(406,454,456)(409,457,453)(412,460,450)(415,463,447)(418,466,444)(421,469,441)(424,472,438)(427,475,435)(429,478,432)(431,482,535)(434,485,532)(437,488,529)(440,491,526)(443,494,523)(446,497,520)(449,500,517)(452,503,514)(455,506,511)(458,509,508)(461,512,505)(464,515,502)(467,518,499)(470,521,496)(473,524,493)(476,527,490)(479,530,487)(481,533,484)(483,537,593)(486,540,590)(489,543,587)(492,546,584)(495,549,581)(498,552,578)(501,555,575)(504,558,572)(507,561,569)(510,564,566)(513,567,563)(516,570,560)(519,573,557)(522,576,554)(525,579,551)(528,582,548)(531,585,545)(534,588,542)(536,591,539)(538,595,654)(541,598,651)(544,601,648)(547,604,645)(550,607,642)(553,610,639)(556,613,636)(559,616,633)(562,619,630)(565,622,627)(568,625,624)(571,628,621)(574,631,618)(577,634,615)(580,637,612)(583,640,609)(586,643,606)(589,646,603)(592,649,600)(594,652,597)(596,656,718)(599,659,715)(602,662,712)(605,665,709)(608,668,706)(611,671,703)(614,674,700)(617,677,697)(620,680,694)(623,683,691)(626,686,688)(629,689,685)(632,692,682)(635,695,679)(638,698,676)(641,701,673)(644,704,670)(647,707,667)(650,710,664)(653,713,661)(655,716,658)(657,720,785)(660,723,782)(663,726,779)(666,729,776)(669,732,773)(672,735,770)(675,738,767)(678,741,764)(681,744,761)(684,747,758)(687,750,755)(690,753,752)(693,756,749)(696,759,746)(699,762,743)(702,765,740)(705,768,737)(708,771,734)(711,774,731)(714,777,728)(717,780,725)(719,783,722)(721,787,788)(724,790,852)(727,793,849)(730,796,846)(733,799,843)(736,802,840)(739,805,837)(742,808,834)(745,811,831)(748,814,828)(751,817,825)(754,820,822)(757,823,819)(760,826,816)(763,829,813)(766,832,810)(769,835,807)(772,838,804)(775,841,801)(778,844,798)(781,847,795)(784,850,792)(786,853,789)(791,858,856)(794,861,920)(797,864,917)(800,867,914)(803,870,911)(806,873,908)(809,876,905)(812,879,902)(815,882,899)(818,885,896)(821,888,893)(824,891,890)(827,894,887)(830,897,884)(833,900,881)(836,903,878)(839,906,875)(842,909,872)(845,912,869)(848,915,866)(851,918,863)(854,921,860)(855,859,857)(862,926,924)(865,929,985)(868,932,982)(871,935,979)(874,938,976)(877,941,973)(880,944,970)(883,947,967)(886,950,964)(889,953,961)(892,956,958)(895,959,955)(898,962,952)(901,965,949)(904,968,946)(907,971,943)(910,974,940)(913,977,937)(916,980,934)(919,983,931)(922,986,928)(923,927,925)(930,991,989)(933,994,1047)(936,997,1044)(939,1000,1041)(942,1003,1038)(945,1006,1035)(948,1009,1032)(951,1012,1029)(954,1015,1026)(957,1018,1023)(960,1021,1020)(963,1024,1017)(966,1027,1014)(969,1030,1011)(972,1033,1008)(975,1036,1005)(978,1039,1002)(981,1042,999)(984,1045,996)(987,1048,993)(988,992,990)(995,1053,1051)(998,1056,1106)(1001,1059,1103)(1004,1062,1100)(1007,1065,1097)(1010,1068,1094)(1013,1071,1091)(1016,1074,1088)(1019,1077,1085)(1022,1080,1082)(1025,1083,1079)(1028,1086,1076)(1031,1089,1073)(1034,1092,1070)(1037,1095,1067)(1040,1098,1064)(1043,1101,1061)(1046,1104,1058)(1049,1107,1055)(1050,1054,1052)(1057,1112,1110)(1060,1115,1162)(1063,1118,1159)(1066,1121,1156)(1069,1124,1153)(1072,1127,1150)(1075,1130,1147)(1078,1133,1144)(1081,1136,1141)(1084,1139,1138)(1087,1142,1135)(1090,1145,1132)(1093,1148,1129)(1096,1151,1126)(1099,1154,1123)(1102,1157,1120)(1105,1160,1117)(1108,1163,1114)(1109,1113,1111)(1116,1168,1166)(1119,1171,1215)(1122,1174,1212)(1125,1177,1209)(1128,1180,1206)(1131,1183,1203)(1134,1186,1200)(1137,1189,1197)(1140,1192,1194)(1143,1195,1191)(1146,1198,1188)(1149,1201,1185)(1152,1204,1182)(1155,1207,1179)(1158,1210,1176)(1161,1213,1173)(1164,1216,1170)(1165,1169,1167)(1172,1221,1219)(1175,1224,1265)(1178,1227,1262)(1181,1230,1259)(1184,1233,1256)(1187,1236,1253)(1190,1239,1250)(1193,1242,1247)(1196,1245,1244)(1199,1248,1241)(1202,1251,1238)(1205,1254,1235)(1208,1257,1232)(1211,1260,1229)(1214,1263,1226)(1217,1266,1223)(1218,1222,1220)(1225,1271,1269)(1228,1274,1312)(1231,1277,1309)(1234,1280,1306)(1237,1283,1303)(1240,1286,1300)(1243,1289,1297)(1246,1292,1294)(1249,1295,1291)(1252,1298,1288)(1255,1301,1285)(1258,1304,1282)(1261,1307,1279)(1264,1310,1276)(1267,1313,1273)(1268,1272,1270)(1275,1318,1316)(1278,1321,1356)(1281,1324,1353)(1284,1327,1350)(1287,1330,1347)(1290,1333,1344)(1293,1336,1341)(1296,1339,1338)(1299,1342,1335)(1302,1345,1332)(1305,1348,1329)(1308,1351,1326)(1311,1354,1323)(1314,1357,1320)(1315,1319,1317)(1322,1362,1360)(1325,1365,1397)(1328,1368,1394)(1331,1371,1391)(1334,1374,1388)(1337,1377,1385)(1340,1380,1382)(1343,1383,1379)(1346,1386,1376)(1349,1389,1373)(1352,1392,1370)(1355,1395,1367)(1358,1398,1364)(1359,1363,1361)(1366,1403,1401)(1369,1406,1435)(1372,1409,1432)(1375,1412,1429)(1378,1415,1426)(1381,1418,1423)(1384,1421,1420)(1387,1424,1417)(1390,1427,1414)(1393,1430,1411)(1396,1433,1408)(1399,1436,1405)(1400,1404,1402)(1407,1441,1439)(1410,1444,1470)(1413,1447,1467)(1416,1450,1464)(1419,1453,1461)(1422,1456,1458)(1425,1459,1455)(1428,1462,1452)(1431,1465,1449)(1434,1468,1446)(1437,1471,1443)(1438,1442,1440)(1445,1476,1474)(1448,1479,1502)(1451,1482,1499)(1454,1485,1496)(1457,1488,1493)(1460,1491,1490)(1463,1494,1487)(1466,1497,1484)(1469,1500,1481)(1472,1503,1478)(1473,1477,1475)(1480,1508,1506)(1483,1511,1531)(1486,1514,1528)(1489,1517,1525)(1492,1520,1522)(1495,1523,1519)(1498,1526,1516)(1501,1529,1513)(1504,1532,1510)(1505,1509,1507)(1512,1537,1535)(1515,1540,1557)(1518,1543,1554)(1521,1546,1551)(1524,1549,1548)(1527,1552,1545)(1530,1555,1542)(1533,1558,1539)(1534,1538,1536)(1541,1563,1561)(1544,1566,1580)(1547,1569,1577)(1550,1572,1574)(1553,1575,1571)(1556,1578,1568)(1559,1581,1565)(1560,1564,1562)(1567,1586,1584)(1570,1589,1600)(1573,1592,1597)(1576,1595,1594)(1579,1598,1591)(1582,1601,1588)(1583,1587,1585)(1590,1606,1604)(1593,1609,1617)(1596,1612,1614)(1599,1615,1611)(1602,1618,1608)(1603,1607,1605)(1610,1623,1621)(1613,1626,1631)(1616,1629,1628)(1619,1632,1625)(1620,1624,1622)(1627,1637,1635)(1630,1640,1642)(1633,1643,1639)(1634,1638,1636)(1641,1648,1646)(1644,1651,1650)(1645,1649,1647)(1652,1656,1654)(1653,1657,1655)(1658,1660,1659);(1,2,3)(4,5,7,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,856,924,989,1051,1110,1166,1219,1269,1316,1360,1401,1439,1474,1506,1535,1561,1584,1604,1621,1635,1646,1654,1659,1656,1640,1612,1572,1520,1456,1380,1292,1192,1080,956,820,686,564,454,356,270,196,134,84,46,20,6,9,14,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,859,785,852,920,985,1047,1106,1162,1215,1265,1312,1356,1397,1435,1470,1502,1531,1557,1580,1600,1617,1631,1642,1650,1655,1648,1626,1592,1546,1488,1418,1336,1242,1136,1018,888,750,622,506,402,310,230,162,106,62,30,10,16,24,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,794,862,927,853,718,782,849,917,982,1044,1103,1159,1212,1262,1309,1353,1394,1432,1467,1499,1528,1554,1577,1597,1614,1628,1639,1647,1637,1609,1569,1517,1453,1377,1289,1189,1077,953,817,683,561,451,353,267,193,131,81,43,17,26,37,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,865,930,992,921,783,654,715,779,846,914,979,1041,1100,1156,1209,1259,1306,1350,1391,1429,1464,1496,1525,1551,1574,1594,1611,1625,1636,1623,1589,1543,1485,1415,1333,1239,1133,1015,885,747,619,503,399,307,227,159,103,59,27,39,53,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,868,933,995,1054,986,850,716,593,651,712,776,843,911,976,1038,1097,1153,1206,1256,1303,1347,1388,1426,1461,1493,1522,1548,1571,1591,1608,1622,1606,1566,1514,1450,1374,1286,1186,1074,950,814,680,558,448,350,264,190,128,78,40,55,72,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,803,871,936,998,1057,1113,1048,918,780,652,535,590,648,709,773,840,908,973,1035,1094,1150,1203,1253,1300,1344,1385,1423,1458,1490,1519,1545,1568,1588,1605,1586,1540,1482,1412,1330,1236,1130,1012,882,744,616,500,396,304,224,156,100,56,74,94,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,806,874,939,1001,1060,1116,1169,1107,983,847,713,591,480,532,587,645,706,770,837,905,970,1032,1091,1147,1200,1250,1297,1341,1382,1420,1455,1487,1516,1542,1565,1585,1563,1511,1447,1371,1283,1183,1071,947,811,677,555,445,347,261,187,125,75,96,119,144,172,203,237,274,314,357,403,452,504,559,617,678,742,809,877,942,1004,1063,1119,1172,1222,1163,1045,915,777,649,533,428,477,529,584,642,70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Conjugacy classes & character table
1665 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29826, 12);
Finite Group Databasebeta