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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1612 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)(721,787,855)(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)(788,857,928)(791,860,925)(794,863,922)(797,866,919)(800,869,916)(803,872,913)(806,875,910)(809,878,907)(812,881,904)(815,884,901)(818,887,898)(821,890,895)(824,893,892)(827,896,889)(830,899,886)(833,902,883)(836,905,880)(839,908,877)(842,911,874)(845,914,871)(848,917,868)(851,920,865)(854,923,862)(856,926,859)(858,930,1003)(861,933,1000)(864,936,997)(867,939,994)(870,942,991)(873,945,988)(876,931,985)(879,950,982)(882,953,979)(885,956,976)(888,959,973)(891,962,970)(894,965,967)(897,968,964)(900,971,961)(903,974,958)(906,977,955)(909,980,952)(912,983,949)(915,986,947)(918,989,944)(921,992,941)(924,995,938)(927,998,935)(929,1001,932)(934,1006,1075)(937,1009,1072)(940,1012,1069)(943,1015,1066)(946,1018,1063)(948,1007,1060)(951,1023,1057)(954,1025,1054)(957,1028,1051)(960,1031,1048)(963,1034,1045)(966,1037,1042)(969,1040,1039)(972,1043,1036)(975,1046,1033)(978,1049,1030)(981,1052,1027)(984,1055,1024)(987,1058,1022)(990,1061,1020)(993,1064,1017)(996,1067,1014)(999,1070,1011)(1002,1073,1008)(1004,1076,1005)(1010,1079,1142)(1013,1082,1139)(1016,1085,1136)(1019,1088,1133)(1021,1080,1130)(1026,1094,1125)(1029,1096,1122)(1032,1099,1119)(1035,1102,1116)(1038,1105,1113)(1041,1108,1110)(1044,1111,1107)(1047,1114,1104)(1050,1117,1101)(1053,1120,1098)(1056,1123,1095)(1059,1126,1093)(1062,1128,1092)(1065,1131,1090)(1068,1134,1087)(1071,1137,1084)(1074,1140,1081)(1077,1143,1078)(1083,1146,1203)(1086,1149,1200)(1089,1152,1197)(1091,1147,1194)(1097,1159,1187)(1100,1161,1184)(1103,1164,1181)(1106,1167,1178)(1109,1170,1175)(1112,1173,1172)(1115,1176,1169)(1118,1179,1166)(1121,1182,1163)(1124,1185,1160)(1127,1188,1158)(1129,1190,1157)(1132,1192,1156)(1135,1195,1154)(1138,1198,1151)(1141,1201,1148)(1144,1204,1145)(1150,1207,1258)(1153,1210,1255)(1155,1208,1252)(1162,1218,1243)(1165,1220,1240)(1168,1223,1237)(1171,1226,1234)(1174,1229,1231)(1177,1232,1228)(1180,1235,1225)(1183,1238,1222)(1186,1241,1219)(1189,1244,1217)(1191,1246,1216)(1193,1248,1215)(1196,1250,1214)(1199,1253,1212)(1202,1256,1209)(1205,1259,1206)(1211,1262,1307)(1213,1263,1304)(1221,1271,1293)(1224,1273,1290)(1227,1276,1287)(1230,1279,1284)(1233,1282,1281)(1236,1285,1278)(1239,1288,1275)(1242,1291,1272)(1245,1294,1270)(1247,1296,1269)(1249,1298,1268)(1251,1300,1267)(1254,1302,1266)(1257,1305,1264)(1260,1308,1261)(1265,1311,1350)(1274,1318,1337)(1277,1320,1334)(1280,1323,1331)(1283,1326,1328)(1286,1329,1325)(1289,1332,1322)(1292,1335,1319)(1295,1338,1317)(1297,1340,1316)(1299,1342,1315)(1301,1344,1314)(1303,1346,1313)(1306,1348,1312)(1309,1351,1310)(1321,1360,1376)(1324,1362,1373)(1327,1365,1370)(1330,1368,1367)(1333,1371,1364)(1336,1374,1361)(1339,1377,1359)(1341,1379,1358)(1343,1381,1357)(1345,1383,1356)(1347,1385,1355)(1349,1387,1354)(1352,1389,1353)(1363,1398,1411)(1366,1400,1408)(1369,1403,1405)(1372,1406,1402)(1375,1409,1399)(1378,1412,1397)(1380,1414,1396)(1382,1416,1395)(1384,1418,1394)(1386,1420,1393)(1388,1422,1392)(1390,1424,1391)(1401,1433,1443)(1404,1435,1440)(1407,1438,1437)(1410,1441,1434)(1413,1444,1432)(1415,1446,1431)(1417,1448,1430)(1419,1450,1429)(1421,1452,1428)(1423,1454,1427)(1425,1456,1426)(1436,1465,1472)(1439,1467,1469)(1442,1470,1466)(1445,1473,1464)(1447,1475,1463)(1449,1477,1462)(1451,1479,1461)(1453,1481,1460)(1455,1483,1459)(1457,1485,1458)(1468,1494,1498)(1471,1496,1495)(1474,1499,1493)(1476,1501,1492)(1478,1503,1491)(1480,1505,1490)(1482,1507,1489)(1484,1509,1488)(1486,1511,1487)(1497,1520,1521)(1500,1522,1519)(1502,1524,1518)(1504,1526,1517)(1506,1528,1516)(1508,1530,1515)(1510,1532,1514)(1512,1534,1513)(1523,1543,1542)(1525,1544,1541)(1527,1546,1540)(1529,1548,1539)(1531,1550,1538)(1533,1552,1537)(1535,1554,1536)(1545,1562,1561)(1547,1563,1560)(1549,1565,1559)(1551,1567,1558)(1553,1569,1557)(1555,1571,1556)(1564,1578,1577)(1566,1579,1576)(1568,1581,1575)(1570,1583,1574)(1572,1585,1573)(1580,1591,1590)(1582,1592,1589)(1584,1594,1588)(1586,1596,1587)(1593,1601,1600)(1595,1602,1599)(1597,1604,1598)(1603,1608,1607)(1605,1609,1606)(1610,1612,1611);(1,2,3)(4,5,7,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,858,931,802,668,546,436,338,252,291,332,375,421,470,522,577,635,696,760,827,897,969,1041,1109,1171,1227,1277,1321,1351,1256,1137,995,850,716,593,651,712,776,843,913,985,1057,1125,1187,1243,1293,1337,1376,1411,1443,1472,1498,1521,1542,1561,1577,1590,1600,1607,1611,1612,1602,1581,1548,1503,1446,1377,1291,1182,1049,902,762,634,518,414,322,242,174,118,73,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,737,804,874,947,1020,1090,1154,1212,1264,1310,1318,1220,1099,956,811,677,555,445,347,261,187,125,75,96,119,144,172,203,237,274,314,357,403,452,504,559,617,678,742,809,879,951,1003,1075,1142,1203,1258,1307,1350,1262,1149,1012,863,723,595,655,717,781,848,918,990,1062,1129,1191,1247,1297,1341,1380,1415,1447,1476,1502,1525,1545,1554,1509,1452,1383,1298,1190,1058,911,771,643,527,423,331,250,287,327,370,416,465,517,572,630,691,755,822,892,964,1036,1104,1166,1222,1272,1317,1358,1395,1429,1460,1488,1513,1520,1467,1403,1326,1229,1108,965,820,686,564,454,356,270,196,134,84,46,20,6,9,14,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,861,934,1007,872,732,604,488,384,292,334,378,424,473,525,580,638,699,763,830,900,972,1044,1112,1174,1230,1280,1324,1363,1389,1305,1198,1067,920,780,652,535,590,648,709,773,840,910,982,1054,1122,1184,1240,1290,1334,1373,1408,1440,1469,1495,1519,1541,1560,1576,1589,1599,1606,1608,1592,1565,1526,1475,1412,1335,1238,1117,974,829,695,573,463,365,279,205,143,93,54,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,670,734,801,871,944,1017,1087,1151,1209,1261,1271,1161,1028,881,741,613,497,393,301,221,153,97,121,147,175,206,240,277,317,360,406,455,507,562,620,681,745,812,882,954,1026,1076,928,1000,1072,1139,1200,1255,1304,1207,1082,936,790,656,719,784,851,921,993,1065,1132,1193,1249,1299,1343,1382,1417,1449,1478,1504,1527,1547,1564,1571,1532,1481,1418,1342,1246,1126,983,838,704,582,472,374,288,213,247,284,324,367,413,462,514,569,627,688,752,819,889,961,1033,1101,1163,1219,1270,1316,1357,1394,1428,1459,1487,1494,1435,1365,1279,1170,1037,890,750,622,506,402,310,230,162,106,62,30,10,16,24,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,794,864,937,1010,1080,945,799,665,543,433,335,380,427,476,528,583,641,702,766,833,903,975,1047,1115,1177,1233,1283,1327,1366,1401,1424,1348,1253,1134,992,847,713,591,480,532,587,645,706,770,837,907,979,1051,1119,1181,1237,1287,1331,1370,1405,1437,1466,1493,1518,1540,1559,1575,1588,1598,1601,1579,1546,1501,1444,1374,1288,1179,1046,899,759,631,515,411,319,239,171,115,71,38,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,667,731,798,868,941,1014,1084,1148,1206,1218,1096,953,808,674,552,442,344,258,184,122,149,178,209,243,280,320,363,409,458,510,565,623,684,748,815,885,957,1029,1097,1143,1001,855,925,997,1069,1136,1197,1252,1146,1009,860,720,786,854,924,996,1068,1135,1196,1251,1301,1345,1384,1419,1451,1480,1506,1529,1549,1566,1580,1585,1552,1507,1450,1381,1296,1188,1055,908,768,640,524,420,328,248,179,210,244,281,321,364,410,459,511,566,624,685,749,816,886,958,1030,1098,1160,1217,1269,1315,1356,1393,1427,1458,1465,1400,1323,1226,1105,962,817,683,561,451,353,267,193,131,81,43,17,26,37,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,867,940,1013,1083,1147,1018,869,729,601,485,381,429,479,531,586,644,705,769,836,906,978,1050,1118,1180,1236,1286,1330,1369,1404,1436,1456,1387,1302,1195,1064,917,777,649,533,428,477,529,584,642,703,767,834,904,976,1048,1116,1178,1234,1284,1328,1367,1402,1434,1464,1492,1517,1539,1558,1574,1587,1591,1563,1524,1473,1409,1332,1235,1114,971,826,692,570,460,362,276,202,140,90,52,25,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,664,728,795,865,938,1011,1081,1145,1159,1025,878,738,610,494,390,298,218,150,180,212,246,283,323,366,412,461,513,568,626,687,751,818,888,960,1032,1100,1162,1204,1073,926,785,852,922,994,1066,1133,1194,1079,933,787,856,927,999,1071,1138,1199,1254,1303,1347,1386,1421,1453,1482,1508,1531,1551,1568,1582,1593,1596,1569,1530,1479,1416,1340,1244,1123,980,835,701,579,469,371,285,211,148,176,207,241,278,318,361,407,456,508,563,621,682,746,813,883,955,1027,1095,1158,1216,1268,1314,1355,1392,1426,1433,1362,1276,1167,1034,887,747,619,503,399,307,227,159,103,59,27,39,53,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,870,943,1016,1086,1150,1208,1088,942,796,662,540,430,481,534,589,647,708,772,839,909,981,1053,1121,1183,1239,1289,1333,1372,1407,1439,1468,1485,1422,1346,1250,1131,989,844,710,588,478,379,425,474,526,581,639,700,764,831,901,973,1045,1113,1175,1231,1281,1325,1364,1399,1432,1463,1491,1516,1538,1557,1573,1578,1544,1499,1441,1371,1285,1176,1043,896,756,628,512,408,316,236,168,112,68,36,15,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,661,725,792,862,935,1008,1078,1094,950,805,671,549,439,341,255,181,214,249,286,326,369,415,464,516,571,629,690,754,821,891,963,1035,1103,1165,1221,1259,1140,998,853,718,782,849,919,991,1063,1130,1006,857,929,1002,1074,1141,1202,1257,1306,1349,1388,1423,1455,1484,1510,1533,1553,1570,1584,1595,1603,1604,1583,1550,1505,1448,1379,1294,1185,1052,905,765,637,521,417,325,245,177,120,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,880,952,1024,1093,1157,1215,1267,1313,1354,1391,1398,1320,1223,1102,959,814,680,558,448,350,264,190,128,78,40,55,72,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,803,873,946,1019,1089,1153,1211,1263,1152,1015,866,726,598,482,536,592,650,711,775,842,912,984,1056,1124,1186,1242,1292,1336,1375,1410,1442,1471,1497,1511,1454,1385,1300,1192,1061,914,774,646,530,426,333,376,422,471,523,578,636,697,761,828,898,970,1042,1110,1172,1228,1278,1322,1361,1397,1431,1462,1490,1515,1537,1556,1562,1522,1470,1406,1329,1232,1111,968,823,689,567,457,359,273,199,137,87,49,23,8,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,658,722,789,859,932,1005,1023,875,735,607,491,387,295,215,251,289,329,372,418,467,519,574,632,693,757,824,894,966,1038,1106,1168,1224,1274,1308,1201,1070,923,783,654,715,779,846,916,988,1060,930,1004,1077,1144,1205,1260,1309,1352,1390,1425,1457,1486,1512,1535,1555,1572,1586,1597,1605,1610,1609,1594,1567,1528,1477,1414,1338,1241,1120,977,832,698,576,466,368,282,208,146,95,117,142,170,201,235,272,312,355,401,450,502,557,615,676,740,807,877,949,1022,1092,1156,1214,1266,1312,1353,1360,1273,1164,1031,884,744,616,500,396,304,224,156,100,56,74,94,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,806,876,948,1021,1091,1155,1213,1265,1311,1210,1085,939,793,659,537,594,653,714,778,845,915,987,1059,1127,1189,1245,1295,1339,1378,1413,1445,1474,1500,1523,1534,1483,1420,1344,1248,1128,986,841,707,585,475,377,290,330,373,419,468,520,575,633,694,758,825,895,967,1039,1107,1169,1225,1275,1319,1359,1396,1430,1461,1489,1514,1536,1543,1496,1438,1368,1282,1173,1040,893,753,625,509,405,313,233,165,109,65,33,13)
Conjugacy classes & character table
1617 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28962, 10);
Finite Group Databasebeta