← Prev (#44565220) Next (#44565222) →
Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1614 points:
(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614);(4,7)(5,6)(9,1614)(10,1613)(11,1612)(12,1611)(13,1610)(14,1609)(15,1608)(16,1607)(17,1606)(18,1605)(19,1604)(20,1603)(21,1602)(22,1601)(23,1600)(24,1599)(25,1598)(26,1597)(27,1596)(28,1595)(29,1594)(30,1593)(31,1592)(32,1591)(33,1590)(34,1589)(35,1588)(36,1587)(37,1586)(38,1585)(39,1584)(40,1583)(41,1582)(42,1581)(43,1580)(44,1579)(45,1578)(46,1577)(47,1576)(48,1575)(49,1574)(50,1573)(51,1572)(52,1571)(53,1570)(54,1569)(55,1568)(56,1567)(57,1566)(58,1565)(59,1564)(60,1563)(61,1562)(62,1561)(63,1560)(64,1559)(65,1558)(66,1557)(67,1556)(68,1555)(69,1554)(70,1553)(71,1552)(72,1551)(73,1550)(74,1549)(75,1548)(76,1547)(77,1546)(78,1545)(79,1544)(80,1543)(81,1542)(82,1541)(83,1540)(84,1539)(85,1538)(86,1537)(87,1536)(88,1535)(89,1534)(90,1533)(91,1532)(92,1531)(93,1530)(94,1529)(95,1528)(96,1527)(97,1526)(98,1525)(99,1524)(100,1523)(101,1522)(102,1521)(103,1520)(104,1519)(105,1518)(106,1517)(107,1516)(108,1515)(109,1514)(110,1513)(111,1512)(112,1511)(113,1510)(114,1509)(115,1508)(116,1507)(117,1506)(118,1505)(119,1504)(120,1503)(121,1502)(122,1501)(123,1500)(124,1499)(125,1498)(126,1497)(127,1496)(128,1495)(129,1494)(130,1493)(131,1492)(132,1491)(133,1490)(134,1489)(135,1488)(136,1487)(137,1486)(138,1485)(139,1484)(140,1483)(141,1482)(142,1481)(143,1480)(144,1479)(145,1478)(146,1477)(147,1476)(148,1475)(149,1474)(150,1473)(151,1472)(152,1471)(153,1470)(154,1469)(155,1468)(156,1467)(157,1466)(158,1465)(159,1464)(160,1463)(161,1462)(162,1461)(163,1460)(164,1459)(165,1458)(166,1457)(167,1456)(168,1455)(169,1454)(170,1453)(171,1452)(172,1451)(173,1450)(174,1449)(175,1448)(176,1447)(177,1446)(178,1445)(179,1444)(180,1443)(181,1442)(182,1441)(183,1440)(184,1439)(185,1438)(186,1437)(187,1436)(188,1435)(189,1434)(190,1433)(191,1432)(192,1431)(193,1430)(194,1429)(195,1428)(196,1427)(197,1426)(198,1425)(199,1424)(200,1423)(201,1422)(202,1421)(203,1420)(204,1419)(205,1418)(206,1417)(207,1416)(208,1415)(209,1414)(210,1413)(211,1412)(212,1411)(213,1410)(214,1409)(215,1408)(216,1407)(217,1406)(218,1405)(219,1404)(220,1403)(221,1402)(222,1401)(223,1400)(224,1399)(225,1398)(226,1397)(227,1396)(228,1395)(229,1394)(230,1393)(231,1392)(232,1391)(233,1390)(234,1389)(235,1388)(236,1387)(237,1386)(238,1385)(239,1384)(240,1383)(241,1382)(242,1381)(243,1380)(244,1379)(245,1378)(246,1377)(247,1376)(248,1375)(249,1374)(250,1373)(251,1372)(252,1371)(253,1370)(254,1369)(255,1368)(256,1367)(257,1366)(258,1365)(259,1364)(260,1363)(261,1362)(262,1361)(263,1360)(264,1359)(265,1358)(266,1357)(267,1356)(268,1355)(269,1354)(270,1353)(271,1352)(272,1351)(273,1350)(274,1349)(275,1348)(276,1347)(277,1346)(278,1345)(279,1344)(280,1343)(281,1342)(282,1341)(283,1340)(284,1339)(285,1338)(286,1337)(287,1336)(288,1335)(289,1334)(290,1333)(291,1332)(292,1331)(293,1330)(294,1329)(295,1328)(296,1327)(297,1326)(298,1325)(299,1324)(300,1323)(301,1322)(302,1321)(303,1320)(304,1319)(305,1318)(306,1317)(307,1316)(308,1315)(309,1314)(310,1313)(311,1312)(312,1311)(313,1310)(314,1309)(315,1308)(316,1307)(317,1306)(318,1305)(319,1304)(320,1303)(321,1302)(322,1301)(323,1300)(324,1299)(325,1298)(326,1297)(327,1296)(328,1295)(329,1294)(330,1293)(331,1292)(332,1291)(333,1290)(334,1289)(335,1288)(336,1287)(337,1286)(338,1285)(339,1284)(340,1283)(341,1282)(342,1281)(343,1280)(344,1279)(345,1278)(346,1277)(347,1276)(348,1275)(349,1274)(350,1273)(351,1272)(352,1271)(353,1270)(354,1269)(355,1268)(356,1267)(357,1266)(358,1265)(359,1264)(360,1263)(361,1262)(362,1261)(363,1260)(364,1259)(365,1258)(366,1257)(367,1256)(368,1255)(369,1254)(370,1253)(371,1252)(372,1251)(373,1250)(374,1249)(375,1248)(376,1247)(377,1246)(378,1245)(379,1244)(380,1243)(381,1242)(382,1241)(383,1240)(384,1239)(385,1238)(386,1237)(387,1236)(388,1235)(389,1234)(390,1233)(391,1232)(392,1231)(393,1230)(394,1229)(395,1228)(396,1227)(397,1226)(398,1225)(399,1224)(400,1223)(401,1222)(402,1221)(403,1220)(404,1219)(405,1218)(406,1217)(407,1216)(408,1215)(409,1214)(410,1213)(411,1212)(412,1211)(413,1210)(414,1209)(415,1208)(416,1207)(417,1206)(418,1205)(419,1204)(420,1203)(421,1202)(422,1201)(423,1200)(424,1199)(425,1198)(426,1197)(427,1196)(428,1195)(429,1194)(430,1193)(431,1192)(432,1191)(433,1190)(434,1189)(435,1188)(436,1187)(437,1186)(438,1185)(439,1184)(440,1183)(441,1182)(442,1181)(443,1180)(444,1179)(445,1178)(446,1177)(447,1176)(448,1175)(449,1174)(450,1173)(451,1172)(452,1171)(453,1170)(454,1169)(455,1168)(456,1167)(457,1166)(458,1165)(459,1164)(460,1163)(461,1162)(462,1161)(463,1160)(464,1159)(465,1158)(466,1157)(467,1156)(468,1155)(469,1154)(470,1153)(471,1152)(472,1151)(473,1150)(474,1149)(475,1148)(476,1147)(477,1146)(478,1145)(479,1144)(480,1143)(481,1142)(482,1141)(483,1140)(484,1139)(485,1138)(486,1137)(487,1136)(488,1135)(489,1134)(490,1133)(491,1132)(492,1131)(493,1130)(494,1129)(495,1128)(496,1127)(497,1126)(498,1125)(499,1124)(500,1123)(501,1122)(502,1121)(503,1120)(504,1119)(505,1118)(506,1117)(507,1116)(508,1115)(509,1114)(510,1113)(511,1112)(512,1111)(513,1110)(514,1109)(515,1108)(516,1107)(517,1106)(518,1105)(519,1104)(520,1103)(521,1102)(522,1101)(523,1100)(524,1099)(525,1098)(526,1097)(527,1096)(528,1095)(529,1094)(530,1093)(531,1092)(532,1091)(533,1090)(534,1089)(535,1088)(536,1087)(537,1086)(538,1085)(539,1084)(540,1083)(541,1082)(542,1081)(543,1080)(544,1079)(545,1078)(546,1077)(547,1076)(548,1075)(549,1074)(550,1073)(551,1072)(552,1071)(553,1070)(554,1069)(555,1068)(556,1067)(557,1066)(558,1065)(559,1064)(560,1063)(561,1062)(562,1061)(563,1060)(564,1059)(565,1058)(566,1057)(567,1056)(568,1055)(569,1054)(570,1053)(571,1052)(572,1051)(573,1050)(574,1049)(575,1048)(576,1047)(577,1046)(578,1045)(579,1044)(580,1043)(581,1042)(582,1041)(583,1040)(584,1039)(585,1038)(586,1037)(587,1036)(588,1035)(589,1034)(590,1033)(591,1032)(592,1031)(593,1030)(594,1029)(595,1028)(596,1027)(597,1026)(598,1025)(599,1024)(600,1023)(601,1022)(602,1021)(603,1020)(604,1019)(605,1018)(606,1017)(607,1016)(608,1015)(609,1014)(610,1013)(611,1012)(612,1011)(613,1010)(614,1009)(615,1008)(616,1007)(617,1006)(618,1005)(619,1004)(620,1003)(621,1002)(622,1001)(623,1000)(624,999)(625,998)(626,997)(627,996)(628,995)(629,994)(630,993)(631,992)(632,991)(633,990)(634,989)(635,988)(636,987)(637,986)(638,985)(639,984)(640,983)(641,982)(642,981)(643,980)(644,979)(645,978)(646,977)(647,976)(648,975)(649,974)(650,973)(651,972)(652,971)(653,970)(654,969)(655,968)(656,967)(657,966)(658,965)(659,964)(660,963)(661,962)(662,961)(663,960)(664,959)(665,958)(666,957)(667,956)(668,955)(669,954)(670,953)(671,952)(672,951)(673,950)(674,949)(675,948)(676,947)(677,946)(678,945)(679,944)(680,943)(681,942)(682,941)(683,940)(684,939)(685,938)(686,937)(687,936)(688,935)(689,934)(690,933)(691,932)(692,931)(693,930)(694,929)(695,928)(696,927)(697,926)(698,925)(699,924)(700,923)(701,922)(702,921)(703,920)(704,919)(705,918)(706,917)(707,916)(708,915)(709,914)(710,913)(711,912)(712,911)(713,910)(714,909)(715,908)(716,907)(717,906)(718,905)(719,904)(720,903)(721,902)(722,901)(723,900)(724,899)(725,898)(726,897)(727,896)(728,895)(729,894)(730,893)(731,892)(732,891)(733,890)(734,889)(735,888)(736,887)(737,886)(738,885)(739,884)(740,883)(741,882)(742,881)(743,880)(744,879)(745,878)(746,877)(747,876)(748,875)(749,874)(750,873)(751,872)(752,871)(753,870)(754,869)(755,868)(756,867)(757,866)(758,865)(759,864)(760,863)(761,862)(762,861)(763,860)(764,859)(765,858)(766,857)(767,856)(768,855)(769,854)(770,853)(771,852)(772,851)(773,850)(774,849)(775,848)(776,847)(777,846)(778,845)(779,844)(780,843)(781,842)(782,841)(783,840)(784,839)(785,838)(786,837)(787,836)(788,835)(789,834)(790,833)(791,832)(792,831)(793,830)(794,829)(795,828)(796,827)(797,826)(798,825)(799,824)(800,823)(801,822)(802,821)(803,820)(804,819)(805,818)(806,817)(807,816)(808,815)(809,814)(810,813)(811,812)
Conjugacy classes & character table
8038 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32140, 11);
Finite Group Databasebeta