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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1582 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)(858,930,1004)(861,933,1001)(864,936,998)(867,939,995)(870,942,992)(873,945,989)(876,948,986)(879,951,983)(882,954,980)(885,957,977)(888,960,974)(891,963,971)(894,966,968)(897,969,965)(900,972,962)(903,975,959)(906,978,956)(909,981,953)(912,984,950)(915,987,947)(918,990,944)(921,993,941)(924,996,938)(927,999,935)(929,1002,932)(931,1006,1039)(934,1008,1079)(937,1011,1076)(940,1014,1073)(943,1017,1070)(946,1020,1067)(949,1023,1064)(952,1026,1061)(955,1029,1058)(958,1032,1055)(961,1035,1052)(964,1038,1049)(967,1041,1046)(970,1044,1043)(973,1047,1040)(976,1050,1037)(979,1053,1034)(982,1056,1031)(985,1059,1028)(988,1062,1025)(991,1065,1022)(994,1068,1019)(997,1071,1016)(1000,1074,1013)(1003,1077,1010)(1005,1080,1007)(1009,1084,1113)(1012,1086,1152)(1015,1089,1149)(1018,1092,1146)(1021,1095,1143)(1024,1098,1140)(1027,1101,1137)(1030,1104,1134)(1033,1107,1131)(1036,1110,1128)(1042,1115,1123)(1045,1118,1120)(1048,1121,1117)(1051,1124,1114)(1054,1126,1112)(1057,1129,1109)(1060,1132,1106)(1063,1135,1103)(1066,1138,1100)(1069,1141,1097)(1072,1144,1094)(1075,1147,1091)(1078,1150,1088)(1081,1153,1085)(1082,1116,1083)(1087,1157,1183)(1090,1159,1219)(1093,1162,1216)(1096,1165,1213)(1099,1168,1210)(1102,1171,1207)(1105,1174,1204)(1108,1177,1201)(1111,1180,1198)(1119,1186,1191)(1122,1189,1188)(1125,1192,1185)(1127,1194,1184)(1130,1196,1182)(1133,1199,1179)(1136,1202,1176)(1139,1205,1173)(1142,1208,1170)(1145,1211,1167)(1148,1214,1164)(1151,1217,1161)(1154,1220,1158)(1155,1187,1156)(1160,1224,1247)(1163,1226,1280)(1166,1229,1277)(1169,1232,1274)(1172,1235,1271)(1175,1238,1268)(1178,1241,1265)(1181,1244,1262)(1190,1251,1253)(1193,1254,1250)(1195,1256,1249)(1197,1258,1248)(1200,1260,1246)(1203,1263,1243)(1206,1266,1240)(1209,1269,1237)(1212,1272,1234)(1215,1275,1231)(1218,1278,1228)(1221,1281,1225)(1222,1252,1223)(1227,1285,1305)(1230,1287,1335)(1233,1290,1332)(1236,1293,1329)(1239,1296,1326)(1242,1299,1323)(1245,1302,1320)(1255,1310,1309)(1257,1312,1308)(1259,1314,1307)(1261,1316,1306)(1264,1318,1304)(1267,1321,1301)(1270,1324,1298)(1273,1327,1295)(1276,1330,1292)(1279,1333,1289)(1282,1336,1286)(1283,1311,1284)(1288,1340,1357)(1291,1342,1384)(1294,1345,1381)(1297,1348,1378)(1300,1351,1375)(1303,1354,1372)(1313,1362,1361)(1315,1364,1360)(1317,1366,1359)(1319,1368,1358)(1322,1370,1356)(1325,1373,1353)(1328,1376,1350)(1331,1379,1347)(1334,1382,1344)(1337,1385,1341)(1338,1363,1339)(1343,1389,1403)(1346,1391,1427)(1349,1394,1424)(1352,1397,1421)(1355,1400,1418)(1365,1408,1407)(1367,1410,1406)(1369,1412,1405)(1371,1414,1404)(1374,1416,1402)(1377,1419,1399)(1380,1422,1396)(1383,1425,1393)(1386,1428,1390)(1387,1409,1388)(1392,1432,1443)(1395,1434,1464)(1398,1437,1461)(1401,1440,1458)(1411,1448,1447)(1413,1450,1446)(1415,1452,1445)(1417,1454,1444)(1420,1456,1442)(1423,1459,1439)(1426,1462,1436)(1429,1465,1433)(1430,1449,1431)(1435,1469,1477)(1438,1471,1495)(1441,1474,1492)(1451,1482,1481)(1453,1484,1480)(1455,1486,1479)(1457,1488,1478)(1460,1490,1476)(1463,1493,1473)(1466,1496,1470)(1467,1483,1468)(1472,1500,1505)(1475,1502,1520)(1485,1510,1509)(1487,1512,1508)(1489,1514,1507)(1491,1516,1506)(1494,1518,1504)(1497,1521,1501)(1498,1511,1499)(1503,1525,1527)(1513,1532,1531)(1515,1534,1530)(1517,1536,1529)(1519,1538,1528)(1522,1540,1526)(1523,1533,1524)(1535,1548,1547)(1537,1550,1546)(1539,1552,1545)(1541,1554,1544)(1542,1549,1543)(1551,1561,1560)(1553,1563,1559)(1555,1565,1558)(1556,1562,1557)(1564,1571,1570)(1566,1573,1569)(1567,1572,1568)(1574,1578,1577)(1575,1579,1576)(1580,1582,1581);(1,2,3)(4,5,7,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,858,931,960,814,680,558,448,350,264,190,128,78,40,55,72,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,803,873,946,1021,1096,1166,1230,1288,1302,1177,1029,878,738,610,494,390,298,218,150,180,212,246,283,323,366,412,461,513,568,626,687,751,818,888,961,1036,1111,1181,1245,1303,1355,1401,1441,1475,1503,1502,1437,1348,1235,1098,945,799,665,543,433,335,380,427,476,528,583,641,702,766,833,903,976,1051,1125,1193,1255,1311,1220,1077,926,785,852,922,995,1070,1143,1210,1271,1326,1375,1418,1389,1287,1162,1014,863,723,595,655,717,781,848,918,991,1066,1139,1206,1267,1322,1371,1415,1453,1485,1511,1465,1382,1275,1144,993,847,713,591,480,532,587,645,706,770,837,907,980,1055,1128,1084,930,1005,1081,1154,1221,1282,1337,1386,1429,1466,1497,1522,1541,1555,1566,1574,1579,1565,1538,1490,1419,1324,1205,1062,911,771,643,527,423,331,250,287,327,370,416,465,517,572,630,691,755,822,892,965,1040,1114,1184,1248,1306,1358,1404,1444,1478,1506,1528,1544,1557,1548,1512,1452,1368,1260,1129,978,832,698,576,466,368,282,208,146,95,117,142,170,201,235,272,312,355,401,450,502,557,615,676,740,807,877,950,1025,1100,1170,1234,1292,1344,1390,1431,1408,1312,1192,1047,896,756,628,512,408,316,236,168,112,68,36,15,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,661,725,792,862,935,1010,1085,1156,1115,963,817,683,561,451,353,267,193,131,81,43,17,26,37,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,867,940,1015,1090,1160,1180,1032,881,741,613,497,393,301,221,153,97,121,147,175,206,240,277,317,360,406,455,507,562,620,681,745,812,882,955,1030,1105,1175,1239,1297,1349,1395,1435,1440,1351,1238,1101,948,802,668,546,436,338,252,291,332,375,421,470,522,577,635,696,760,827,897,970,1045,1119,1187,1080,928,1001,1076,1149,1216,1277,1332,1381,1424,1461,1492,1469,1391,1290,1165,1017,866,726,598,482,536,592,650,711,775,842,912,985,1060,1133,1200,1261,1317,1367,1411,1449,1385,1278,1147,996,850,716,593,651,712,776,843,913,986,1061,1134,1201,1262,1224,1086,933,787,856,927,1000,1075,1148,1215,1276,1331,1380,1423,1460,1491,1517,1537,1551,1562,1540,1493,1422,1327,1208,1065,914,774,646,530,426,333,376,422,471,523,578,636,697,761,828,898,971,1046,1120,1188,1250,1308,1360,1406,1446,1480,1508,1530,1546,1559,1569,1576,1571,1550,1514,1454,1370,1263,1132,981,835,701,579,469,371,285,211,148,176,207,241,278,318,361,407,456,508,563,621,682,746,813,883,956,1031,1106,1176,1240,1298,1350,1396,1436,1470,1499,1482,1410,1314,1194,1050,899,759,631,515,411,319,239,171,115,71,38,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,667,731,798,868,941,1016,1091,1161,1225,1284,1251,1118,966,820,686,564,454,356,270,196,134,84,46,20,6,9,14,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,861,934,1009,1035,884,744,616,500,396,304,224,156,100,56,74,94,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,806,876,949,1024,1099,1169,1233,1291,1343,1354,1241,1104,951,805,671,549,439,341,255,181,214,249,286,326,369,415,464,516,571,629,690,754,821,891,964,1039,1113,1183,1247,1305,1357,1403,1443,1477,1505,1527,1525,1471,1394,1293,1168,1020,869,729,601,485,381,429,479,531,586,644,705,769,836,906,979,1054,1127,1195,1257,1313,1363,1281,1150,999,853,718,782,849,919,992,1067,1140,1207,1268,1323,1372,1340,1226,1089,936,790,656,719,784,851,921,994,1069,1142,1209,1270,1325,1374,1417,1455,1487,1513,1533,1496,1425,1330,1211,1068,917,777,649,533,428,477,529,584,642,703,767,834,904,977,1052,1006,1082,1155,1222,1283,1338,1387,1430,1467,1498,1523,1542,1556,1567,1575,1580,1582,1573,1552,1516,1456,1373,1266,1135,984,838,704,582,472,374,288,213,247,284,324,367,413,462,514,569,627,688,752,819,889,962,1037,1112,1182,1246,1304,1356,1402,1442,1476,1504,1526,1543,1532,1484,1412,1316,1196,1053,902,762,634,518,414,322,242,174,118,73,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,737,804,874,947,1022,1097,1167,1231,1289,1341,1388,1362,1254,1121,969,823,689,567,457,359,273,199,137,87,49,23,8,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,658,722,789,859,932,1007,1083,1038,887,747,619,503,399,307,227,159,103,59,27,39,53,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,870,943,1018,1093,1163,1227,1244,1107,954,808,674,552,442,344,258,184,122,149,178,209,243,280,320,363,409,458,510,565,623,684,748,815,885,958,1033,1108,1178,1242,1300,1352,1398,1438,1472,1474,1397,1296,1171,1023,872,732,604,488,384,292,334,378,424,473,525,580,638,699,763,830,900,973,1048,1122,1190,1252,1153,1002,855,925,998,1073,1146,1213,1274,1329,1378,1421,1458,1432,1342,1229,1092,939,793,659,537,594,653,714,778,845,915,988,1063,1136,1203,1264,1319,1369,1413,1451,1483,1428,1333,1214,1071,920,780,652,535,590,648,709,773,840,910,983,1058,1131,1198,1157,1008,857,929,1003,1078,1151,1218,1279,1334,1383,1426,1463,1494,1519,1539,1553,1564,1572,1554,1518,1459,1376,1269,1138,987,841,707,585,475,377,290,330,373,419,468,520,575,633,694,758,825,895,968,1043,1117,1185,1249,1307,1359,1405,1445,1479,1507,1529,1545,1558,1568,1561,1534,1486,1414,1318,1199,1056,905,765,637,521,417,325,245,177,120,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,880,953,1028,1103,1173,1237,1295,1347,1393,1433,1468,1448,1364,1256,1124,972,826,692,570,460,362,276,202,140,90,52,25,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,664,728,795,865,938,1013,1088,1158,1223,1186,1041,890,750,622,506,402,310,230,162,106,62,30,10,16,24,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,794,864,937,1012,1087,1110,957,811,677,555,445,347,261,187,125,75,96,119,144,172,203,237,274,314,357,403,452,504,559,617,678,742,809,879,952,1027,1102,1172,1236,1294,1346,1392,1400,1299,1174,1026,875,735,607,491,387,295,215,251,289,329,372,418,467,519,574,632,693,757,824,894,967,1042,1116,1004,1079,1152,1219,1280,1335,1384,1427,1464,1495,1520,1500,1434,1345,1232,1095,942,796,662,540,430,481,534,589,647,708,772,839,909,982,1057,1130,1197,1259,1315,1365,1409,1336,1217,1074,923,783,654,715,779,846,916,989,1064,1137,1204,1265,1320,1285,1159,1011,860,720,786,854,924,997,1072,1145,1212,1273,1328,1377,1420,1457,1489,1515,1535,1549,1521,1462,1379,1272,1141,990,844,710,588,478,379,425,474,526,581,639,700,764,831,901,974,1049,1123,1191,1253,1309,1361,1407,1447,1481,1509,1531,1547,1560,1570,1577,1581,1578,1563,1536,1488,1416,1321,1202,1059,908,768,640,524,420,328,248,179,210,244,281,321,364,410,459,511,566,624,685,749,816,886,959,1034,1109,1179,1243,1301,1353,1399,1439,1473,1501,1524,1510,1450,1366,1258,1126,975,829,695,573,463,365,279,205,143,93,54,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,670,734,801,871,944,1019,1094,1164,1228,1286,1339,1310,1189,1044,893,753,625,509,405,313,233,165,109,65,33,13)
Conjugacy classes & character table
1587 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28422, 10);
Finite Group Databasebeta