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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1608 points:
(3,4,5,6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)(847,848)(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)(863,864)(865,866)(867,868)(869,870)(871,872)(873,874)(875,876)(877,878)(879,880)(881,882)(883,884)(885,886)(887,888)(889,890)(891,892)(893,894)(895,896)(897,898)(899,900)(901,902)(903,904)(905,906)(907,908)(909,910)(911,912)(913,914)(915,916)(917,918)(919,920)(921,922)(923,924)(925,926)(927,928)(929,930)(931,932)(933,934)(935,936)(937,938)(939,940)(941,942)(943,944)(945,946)(947,948)(949,950)(951,952)(953,954)(955,956)(957,958)(959,960)(961,962)(963,964)(965,966)(967,968)(969,970)(971,972)(973,974)(975,976)(977,978)(979,980)(981,982)(983,984)(985,986)(987,988)(989,990)(991,992)(993,994)(995,996)(997,998)(999,1000)(1001,1002)(1003,1004)(1005,1006)(1007,1008)(1009,1010)(1011,1012)(1013,1014)(1015,1016)(1017,1018)(1019,1020)(1021,1022)(1023,1024)(1025,1026)(1027,1028)(1029,1030)(1031,1032)(1033,1034)(1035,1036)(1037,1038)(1039,1040)(1041,1042)(1043,1044)(1045,1046)(1047,1048)(1049,1050)(1051,1052)(1053,1054)(1055,1056)(1057,1058)(1059,1060)(1061,1062)(1063,1064)(1065,1066)(1067,1068)(1069,1070)(1071,1072)(1073,1074)(1075,1076)(1077,1078)(1079,1080)(1081,1082)(1083,1084)(1085,1086)(1087,1088)(1089,1090)(1091,1092)(1093,1094)(1095,1096)(1097,1098)(1099,1100)(1101,1102)(1103,1104)(1105,1106)(1107,1108)(1109,1110)(1111,1112)(1113,1114)(1115,1116)(1117,1118)(1119,1120)(1121,1122)(1123,1124)(1125,1126)(1127,1128)(1129,1130)(1131,1132)(1133,1134)(1135,1136)(1137,1138)(1139,1140)(1141,1142)(1143,1144)(1145,1146)(1147,1148)(1149,1150)(1151,1152)(1153,1154)(1155,1156)(1157,1158)(1159,1160)(1161,1162)(1163,1164)(1165,1166)(1167,1168)(1169,1170)(1171,1172)(1173,1174)(1175,1176)(1177,1178)(1179,1180)(1181,1182)(1183,1184)(1185,1186)(1187,1188)(1189,1190)(1191,1192)(1193,1194)(1195,1196)(1197,1198)(1199,1200)(1201,1202)(1203,1204)(1205,1206)(1207,1208)(1209,1210)(1211,1212)(1213,1214)(1215,1216)(1217,1218)(1219,1220)(1221,1222)(1223,1224)(1225,1226)(1227,1228)(1229,1230)(1231,1232)(1233,1234)(1235,1236)(1237,1238)(1239,1240)(1241,1242)(1243,1244)(1245,1246)(1247,1248)(1249,1250)(1251,1252)(1253,1254)(1255,1256)(1257,1258)(1259,1260)(1261,1262)(1263,1264)(1265,1266)(1267,1268)(1269,1270)(1271,1272)(1273,1274)(1275,1276)(1277,1278)(1279,1280)(1281,1282)(1283,1284)(1285,1286)(1287,1288)(1289,1290)(1291,1292)(1293,1294)(1295,1296)(1297,1298)(1299,1300)(1301,1302)(1303,1304)(1305,1306)(1307,1308)(1309,1310)(1311,1312)(1313,1314)(1315,1316)(1317,1318)(1319,1320)(1321,1322)(1323,1324)(1325,1326)(1327,1328)(1329,1330)(1331,1332)(1333,1334)(1335,1336)(1337,1338)(1339,1340)(1341,1342)(1343,1344)(1345,1346)(1347,1348)(1349,1350)(1351,1352)(1353,1354)(1355,1356)(1357,1358)(1359,1360)(1361,1362)(1363,1364)(1365,1366)(1367,1368)(1369,1370)(1371,1372)(1373,1374)(1375,1376)(1377,1378)(1379,1380)(1381,1382)(1383,1384)(1385,1386)(1387,1388)(1389,1390)(1391,1392)(1393,1394)(1395,1396)(1397,1398)(1399,1400)(1401,1402)(1403,1404)(1405,1406)(1407,1408)(1409,1410)(1411,1412)(1413,1414)(1415,1416)(1417,1418)(1419,1420)(1421,1422)(1423,1424)(1425,1426)(1427,1428)(1429,1430)(1431,1432)(1433,1434)(1435,1436)(1437,1438)(1439,1440)(1441,1442)(1443,1444)(1445,1446)(1447,1448)(1449,1450)(1451,1452)(1453,1454)(1455,1456)(1457,1458)(1459,1460)(1461,1462)(1463,1464)(1465,1466)(1467,1468)(1469,1470)(1471,1472)(1473,1474)(1475,1476)(1477,1478)(1479,1480)(1481,1482)(1483,1484)(1485,1486)(1487,1488)(1489,1490)(1491,1492)(1493,1494)(1495,1496)(1497,1498)(1499,1500)(1501,1502)(1503,1504)(1505,1506)(1507,1508)(1509,1510)(1511,1512)(1513,1514)(1515,1516)(1517,1518)(1519,1520)(1521,1522)(1523,1524)(1525,1526)(1527,1528)(1529,1530)(1531,1532)(1533,1534)(1535,1536)(1537,1538)(1539,1540)(1541,1542)(1543,1544)(1545,1546)(1547,1548)(1549,1550)(1551,1552)(1553,1554)(1555,1556)(1557,1558)(1559,1560)(1561,1562)(1563,1564)(1565,1566)(1567,1568)(1569,1570)(1571,1572)(1573,1574)(1575,1576)(1577,1578)(1579,1580)(1581,1582)(1583,1584)(1585,1586)(1587,1588)(1589,1590)(1591,1592)(1593,1594)(1595,1596)(1597,1598)(1599,1600)(1601,1602)(1603,1604)(1605,1606)(1607,1608);(1,2)(8,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,135,137,139,141,143,145,147,149,151,153,155,157,159,161,163,165,167,169,171,173,175,177,179,181,183,185,187,189,191,193,195,197,199,201,203,205,207,209,211,213,215,217,219,221,223,225,227,229,231,233,235,237,239,241,243,245,247,249,251,253,255,257,259,261,263,265,267,269,271,273,275,277,279,281,283,285,287,289,291,293,295,297,299,301,303,305,307,309,311,313,315,317,319,321,323,325,327,329,331,333,335,337,339,341,343,345,347,349,351,353,355,357,359,361,363,365,367,369,371,373,375,377,379,381,383,385,387,389,391,393,395,397,399,401,403,405,407,409,411,413,415,417,419,421,423,425,427,429,431,433,435,437,439,441,443,445,447,449,451,453,455,457,459,461,463,465,467,469,471,473,475,477,479,481,483,485,487,489,491,493,495,497,499,501,503,505,507,509,511,513,515,517,519,521,523,525,527,529,531,533,535,537,539,541,543,545,547,549,551,553,555,557,559,561,563,565,567,569,571,573,575,577,579,581,583,585,587,589,591,593,595,597,599,601,603,605,607,609,611,613,615,617,619,621,623,625,627,629,631,633,635,637,639,641,643,645,647,649,651,653,655,657,659,661,663,665,667,669,671,673,675,677,679,681,683,685,687,689,691,693,695,697,699,701,703,705,707,709,711,713,715,717,719,721,723,725,727,729,731,733,735,737,739,741,743,745,747,749,751,753,755,757,759,761,763,765,767,769,771,773,775,777,779,781,783,785,787,789,791,793,795,797,799,801,803,805,807,809,811,813,815,817,819,821,823,825,827,829,831,833,835,837,839,841,843,845,847,849,851,853,855,857,859,861,863,865,867,869,871,873,875,877,879,881,883,885,887,889,891,893,895,897,899,901,903,905,907,909,911,913,915,917,919,921,923,925,927,929,931,933,935,937,939,941,943,945,947,949,951,953,955,957,959,961,963,965,967,969,971,973,975,977,979,981,983,985,987,989,991,993,995,997,999,1001,1003,1005,1007,1009,1011,1013,1015,1017,1019,1021,1023,1025,1027,1029,1031,1033,1035,1037,1039,1041,1043,1045,1047,1049,1051,1053,1055,1057,1059,1061,1063,1065,1067,1069,1071,1073,1075,1077,1079,1081,1083,1085,1087,1089,1091,1093,1095,1097,1099,1101,1103,1105,1107,1109,1111,1113,1115,1117,1119,1121,1123,1125,1127,1129,1131,1133,1135,1137,1139,1141,1143,1145,1147,1149,1151,1153,1155,1157,1159,1161,1163,1165,1167,1169,1171,1173,1175,1177,1179,1181,1183,1185,1187,1189,1191,1193,1195,1197,1199,1201,1203,1205,1207,1209,1211,1213,1215,1217,1219,1221,1223,1225,1227,1229,1231,1233,1235,1237,1239,1241,1243,1245,1247,1249,1251,1253,1255,1257,1259,1261,1263,1265,1267,1269,1271,1273,1275,1277,1279,1281,1283,1285,1287,1289,1291,1293,1295,1297,1299,1301,1303,1305,1307,1309,1311,1313,1315,1317,1319,1321,1323,1325,1327,1329,1331,1333,1335,1337,1339,1341,1343,1345,1347,1349,1351,1353,1355,1357,1359,1361,1363,1365,1367,1369,1371,1373,1375,1377,1379,1381,1383,1385,1387,1389,1391,1393,1395,1397,1399,1401,1403,1405,1407,1409,1411,1413,1415,1417,1419,1421,1423,1425,1427,1429,1431,1433,1435,1437,1439,1441,1443,1445,1447,1449,1451,1453,1455,1457,1459,1461,1463,1465,1467,1469,1471,1473,1475,1477,1479,1481,1483,1485,1487,1489,1491,1493,1495,1497,1499,1501,1503,1505,1507,1509,1511,1513,1515,1517,1519,1521,1523,1525,1527,1529,1531,1533,1535,1537,1539,1541,1543,1545,1547,1549,1551,1553,1555,1557,1559,1561,1563,1565,1567,1569,1571,1573,1575,1577,1579,1581,1583,1585,1587,1589,1591,1593,1595,1597,1599,1601,1603,1605,1607,1608,1606,1604,1602,1600,1598,1596,1594,1592,1590,1588,1586,1584,1582,1580,1578,1576,1574,1572,1570,1568,1566,1564,1562,1560,1558,1556,1554,1552,1550,1548,1546,1544,1542,1540,1538,1536,1534,1532,1530,1528,1526,1524,1522,1520,1518,1516,1514,1512,1510,1508,1506,1504,1502,1500,1498,1496,1494,1492,1490,1488,1486,1484,1482,1480,1478,1476,1474,1472,1470,1468,1466,1464,1462,1460,1458,1456,1454,1452,1450,1448,1446,1444,1442,1440,1438,1436,1434,1432,1430,1428,1426,1424,1422,1420,1418,1416,1414,1412,1410,1408,1406,1404,1402,1400,1398,1396,1394,1392,1390,1388,1386,1384,1382,1380,1378,1376,1374,1372,1370,1368,1366,1364,1362,1360,1358,1356,1354,1352,1350,1348,1346,1344,1342,1340,1338,1336,1334,1332,1330,1328,1326,1324,1322,1320,1318,1316,1314,1312,1310,1308,1306,1304,1302,1300,1298,1296,1294,1292,1290,1288,1286,1284,1282,1280,1278,1276,1274,1272,1270,1268,1266,1264,1262,1260,1258,1256,1254,1252,1250,1248,1246,1244,1242,1240,1238,1236,1234,1232,1230,1228,1226,1224,1222,1220,1218,1216,1214,1212,1210,1208,1206,1204,1202,1200,1198,1196,1194,1192,1190,1188,1186,1184,1182,1180,1178,1176,1174,1172,1170,1168,1166,1164,1162,1160,1158,1156,1154,1152,1150,1148,1146,1144,1142,1140,1138,1136,1134,1132,1130,1128,1126,1124,1122,1120,1118,1116,1114,1112,1110,1108,1106,1104,1102,1100,1098,1096,1094,1092,1090,1088,1086,1084,1082,1080,1078,1076,1074,1072,1070,1068,1066,1064,1062,1060,1058,1056,1054,1052,1050,1048,1046,1044,1042,1040,1038,1036,1034,1032,1030,1028,1026,1024,1022,1020,1018,1016,1014,1012,1010,1008,1006,1004,1002,1000,998,996,994,992,990,988,986,984,982,980,978,976,974,972,970,968,966,964,962,960,958,956,954,952,950,948,946,944,942,940,938,936,934,932,930,928,926,924,922,920,918,916,914,912,910,908,906,904,902,900,898,896,894,892,890,888,886,884,882,880,878,876,874,872,870,868,866,864,862,860,858,856,854,852,850,848,846,844,842,840,838,836,834,832,830,828,826,824,822,820,818,816,814,812,810,808,806,804,802,800,798,796,794,792,790,788,786,784,782,780,778,776,774,772,770,768,766,764,762,760,758,756,754,752,750,748,746,744,742,740,738,736,734,732,730,728,726,724,722,720,718,716,714,712,710,708,706,704,702,700,698,696,694,692,690,688,686,684,682,680,678,676,674,672,670,668,666,664,662,660,658,656,654,652,650,648,646,644,642,640,638,636,634,632,630,628,626,624,622,620,618,616,614,612,610,608,606,604,602,600,598,596,594,592,590,588,586,584,582,580,578,576,574,572,570,568,566,564,562,560,558,556,554,552,550,548,546,544,542,540,538,536,534,532,530,528,526,524,522,520,518,516,514,512,510,508,506,504,502,500,498,496,494,492,490,488,486,484,482,480,478,476,474,472,470,468,466,464,462,460,458,456,454,452,450,448,446,444,442,440,438,436,434,432,430,428,426,424,422,420,418,416,414,412,410,408,406,404,402,400,398,396,394,392,390,388,386,384,382,380,378,376,374,372,370,368,366,364,362,360,358,356,354,352,350,348,346,344,342,340,338,336,334,332,330,328,326,324,322,320,318,316,314,312,310,308,306,304,302,300,298,296,294,292,290,288,286,284,282,280,278,276,274,272,270,268,266,264,262,260,258,256,254,252,250,248,246,244,242,240,238,236,234,232,230,228,226,224,222,220,218,216,214,212,210,208,206,204,202,200,198,196,194,192,190,188,186,184,182,180,178,176,174,172,170,168,166,164,162,160,158,156,154,152,150,148,146,144,142,140,138,136,134,132,130,128,126,124,122,120,118,116,114,112,110,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10)
Conjugacy classes & character table
8020 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32020, 18);
Finite Group Databasebeta