← Prev (#36319306) Next (#36319308) →
Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1782 points:
(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782);(4,5)(7,1782)(8,1781)(9,1780)(10,1779)(11,1778)(12,1777)(13,1776)(14,1775)(15,1774)(16,1773)(17,1772)(18,1771)(19,1770)(20,1769)(21,1768)(22,1767)(23,1766)(24,1765)(25,1764)(26,1763)(27,1762)(28,1761)(29,1760)(30,1759)(31,1758)(32,1757)(33,1756)(34,1755)(35,1754)(36,1753)(37,1752)(38,1751)(39,1750)(40,1749)(41,1748)(42,1747)(43,1746)(44,1745)(45,1744)(46,1743)(47,1742)(48,1741)(49,1740)(50,1739)(51,1738)(52,1737)(53,1736)(54,1735)(55,1734)(56,1733)(57,1732)(58,1731)(59,1730)(60,1729)(61,1728)(62,1727)(63,1726)(64,1725)(65,1724)(66,1723)(67,1722)(68,1721)(69,1720)(70,1719)(71,1718)(72,1717)(73,1716)(74,1715)(75,1714)(76,1713)(77,1712)(78,1711)(79,1710)(80,1709)(81,1708)(82,1707)(83,1706)(84,1705)(85,1704)(86,1703)(87,1702)(88,1701)(89,1700)(90,1699)(91,1698)(92,1697)(93,1696)(94,1695)(95,1694)(96,1693)(97,1692)(98,1691)(99,1690)(100,1689)(101,1688)(102,1687)(103,1686)(104,1685)(105,1684)(106,1683)(107,1682)(108,1681)(109,1680)(110,1679)(111,1678)(112,1677)(113,1676)(114,1675)(115,1674)(116,1673)(117,1672)(118,1671)(119,1670)(120,1669)(121,1668)(122,1667)(123,1666)(124,1665)(125,1664)(126,1663)(127,1662)(128,1661)(129,1660)(130,1659)(131,1658)(132,1657)(133,1656)(134,1655)(135,1654)(136,1653)(137,1652)(138,1651)(139,1650)(140,1649)(141,1648)(142,1647)(143,1646)(144,1645)(145,1644)(146,1643)(147,1642)(148,1641)(149,1640)(150,1639)(151,1638)(152,1637)(153,1636)(154,1635)(155,1634)(156,1633)(157,1632)(158,1631)(159,1630)(160,1629)(161,1628)(162,1627)(163,1626)(164,1625)(165,1624)(166,1623)(167,1622)(168,1621)(169,1620)(170,1619)(171,1618)(172,1617)(173,1616)(174,1615)(175,1614)(176,1613)(177,1612)(178,1611)(179,1610)(180,1609)(181,1608)(182,1607)(183,1606)(184,1605)(185,1604)(186,1603)(187,1602)(188,1601)(189,1600)(190,1599)(191,1598)(192,1597)(193,1596)(194,1595)(195,1594)(196,1593)(197,1592)(198,1591)(199,1590)(200,1589)(201,1588)(202,1587)(203,1586)(204,1585)(205,1584)(206,1583)(207,1582)(208,1581)(209,1580)(210,1579)(211,1578)(212,1577)(213,1576)(214,1575)(215,1574)(216,1573)(217,1572)(218,1571)(219,1570)(220,1569)(221,1568)(222,1567)(223,1566)(224,1565)(225,1564)(226,1563)(227,1562)(228,1561)(229,1560)(230,1559)(231,1558)(232,1557)(233,1556)(234,1555)(235,1554)(236,1553)(237,1552)(238,1551)(239,1550)(240,1549)(241,1548)(242,1547)(243,1546)(244,1545)(245,1544)(246,1543)(247,1542)(248,1541)(249,1540)(250,1539)(251,1538)(252,1537)(253,1536)(254,1535)(255,1534)(256,1533)(257,1532)(258,1531)(259,1530)(260,1529)(261,1528)(262,1527)(263,1526)(264,1525)(265,1524)(266,1523)(267,1522)(268,1521)(269,1520)(270,1519)(271,1518)(272,1517)(273,1516)(274,1515)(275,1514)(276,1513)(277,1512)(278,1511)(279,1510)(280,1509)(281,1508)(282,1507)(283,1506)(284,1505)(285,1504)(286,1503)(287,1502)(288,1501)(289,1500)(290,1499)(291,1498)(292,1497)(293,1496)(294,1495)(295,1494)(296,1493)(297,1492)(298,1491)(299,1490)(300,1489)(301,1488)(302,1487)(303,1486)(304,1485)(305,1484)(306,1483)(307,1482)(308,1481)(309,1480)(310,1479)(311,1478)(312,1477)(313,1476)(314,1475)(315,1474)(316,1473)(317,1472)(318,1471)(319,1470)(320,1469)(321,1468)(322,1467)(323,1466)(324,1465)(325,1464)(326,1463)(327,1462)(328,1461)(329,1460)(330,1459)(331,1458)(332,1457)(333,1456)(334,1455)(335,1454)(336,1453)(337,1452)(338,1451)(339,1450)(340,1449)(341,1448)(342,1447)(343,1446)(344,1445)(345,1444)(346,1443)(347,1442)(348,1441)(349,1440)(350,1439)(351,1438)(352,1437)(353,1436)(354,1435)(355,1434)(356,1433)(357,1432)(358,1431)(359,1430)(360,1429)(361,1428)(362,1427)(363,1426)(364,1425)(365,1424)(366,1423)(367,1422)(368,1421)(369,1420)(370,1419)(371,1418)(372,1417)(373,1416)(374,1415)(375,1414)(376,1413)(377,1412)(378,1411)(379,1410)(380,1409)(381,1408)(382,1407)(383,1406)(384,1405)(385,1404)(386,1403)(387,1402)(388,1401)(389,1400)(390,1399)(391,1398)(392,1397)(393,1396)(394,1395)(395,1394)(396,1393)(397,1392)(398,1391)(399,1390)(400,1389)(401,1388)(402,1387)(403,1386)(404,1385)(405,1384)(406,1383)(407,1382)(408,1381)(409,1380)(410,1379)(411,1378)(412,1377)(413,1376)(414,1375)(415,1374)(416,1373)(417,1372)(418,1371)(419,1370)(420,1369)(421,1368)(422,1367)(423,1366)(424,1365)(425,1364)(426,1363)(427,1362)(428,1361)(429,1360)(430,1359)(431,1358)(432,1357)(433,1356)(434,1355)(435,1354)(436,1353)(437,1352)(438,1351)(439,1350)(440,1349)(441,1348)(442,1347)(443,1346)(444,1345)(445,1344)(446,1343)(447,1342)(448,1341)(449,1340)(450,1339)(451,1338)(452,1337)(453,1336)(454,1335)(455,1334)(456,1333)(457,1332)(458,1331)(459,1330)(460,1329)(461,1328)(462,1327)(463,1326)(464,1325)(465,1324)(466,1323)(467,1322)(468,1321)(469,1320)(470,1319)(471,1318)(472,1317)(473,1316)(474,1315)(475,1314)(476,1313)(477,1312)(478,1311)(479,1310)(480,1309)(481,1308)(482,1307)(483,1306)(484,1305)(485,1304)(486,1303)(487,1302)(488,1301)(489,1300)(490,1299)(491,1298)(492,1297)(493,1296)(494,1295)(495,1294)(496,1293)(497,1292)(498,1291)(499,1290)(500,1289)(501,1288)(502,1287)(503,1286)(504,1285)(505,1284)(506,1283)(507,1282)(508,1281)(509,1280)(510,1279)(511,1278)(512,1277)(513,1276)(514,1275)(515,1274)(516,1273)(517,1272)(518,1271)(519,1270)(520,1269)(521,1268)(522,1267)(523,1266)(524,1265)(525,1264)(526,1263)(527,1262)(528,1261)(529,1260)(530,1259)(531,1258)(532,1257)(533,1256)(534,1255)(535,1254)(536,1253)(537,1252)(538,1251)(539,1250)(540,1249)(541,1248)(542,1247)(543,1246)(544,1245)(545,1244)(546,1243)(547,1242)(548,1241)(549,1240)(550,1239)(551,1238)(552,1237)(553,1236)(554,1235)(555,1234)(556,1233)(557,1232)(558,1231)(559,1230)(560,1229)(561,1228)(562,1227)(563,1226)(564,1225)(565,1224)(566,1223)(567,1222)(568,1221)(569,1220)(570,1219)(571,1218)(572,1217)(573,1216)(574,1215)(575,1214)(576,1213)(577,1212)(578,1211)(579,1210)(580,1209)(581,1208)(582,1207)(583,1206)(584,1205)(585,1204)(586,1203)(587,1202)(588,1201)(589,1200)(590,1199)(591,1198)(592,1197)(593,1196)(594,1195)(595,1194)(596,1193)(597,1192)(598,1191)(599,1190)(600,1189)(601,1188)(602,1187)(603,1186)(604,1185)(605,1184)(606,1183)(607,1182)(608,1181)(609,1180)(610,1179)(611,1178)(612,1177)(613,1176)(614,1175)(615,1174)(616,1173)(617,1172)(618,1171)(619,1170)(620,1169)(621,1168)(622,1167)(623,1166)(624,1165)(625,1164)(626,1163)(627,1162)(628,1161)(629,1160)(630,1159)(631,1158)(632,1157)(633,1156)(634,1155)(635,1154)(636,1153)(637,1152)(638,1151)(639,1150)(640,1149)(641,1148)(642,1147)(643,1146)(644,1145)(645,1144)(646,1143)(647,1142)(648,1141)(649,1140)(650,1139)(651,1138)(652,1137)(653,1136)(654,1135)(655,1134)(656,1133)(657,1132)(658,1131)(659,1130)(660,1129)(661,1128)(662,1127)(663,1126)(664,1125)(665,1124)(666,1123)(667,1122)(668,1121)(669,1120)(670,1119)(671,1118)(672,1117)(673,1116)(674,1115)(675,1114)(676,1113)(677,1112)(678,1111)(679,1110)(680,1109)(681,1108)(682,1107)(683,1106)(684,1105)(685,1104)(686,1103)(687,1102)(688,1101)(689,1100)(690,1099)(691,1098)(692,1097)(693,1096)(694,1095)(695,1094)(696,1093)(697,1092)(698,1091)(699,1090)(700,1089)(701,1088)(702,1087)(703,1086)(704,1085)(705,1084)(706,1083)(707,1082)(708,1081)(709,1080)(710,1079)(711,1078)(712,1077)(713,1076)(714,1075)(715,1074)(716,1073)(717,1072)(718,1071)(719,1070)(720,1069)(721,1068)(722,1067)(723,1066)(724,1065)(725,1064)(726,1063)(727,1062)(728,1061)(729,1060)(730,1059)(731,1058)(732,1057)(733,1056)(734,1055)(735,1054)(736,1053)(737,1052)(738,1051)(739,1050)(740,1049)(741,1048)(742,1047)(743,1046)(744,1045)(745,1044)(746,1043)(747,1042)(748,1041)(749,1040)(750,1039)(751,1038)(752,1037)(753,1036)(754,1035)(755,1034)(756,1033)(757,1032)(758,1031)(759,1030)(760,1029)(761,1028)(762,1027)(763,1026)(764,1025)(765,1024)(766,1023)(767,1022)(768,1021)(769,1020)(770,1019)(771,1018)(772,1017)(773,1016)(774,1015)(775,1014)(776,1013)(777,1012)(778,1011)(779,1010)(780,1009)(781,1008)(782,1007)(783,1006)(784,1005)(785,1004)(786,1003)(787,1002)(788,1001)(789,1000)(790,999)(791,998)(792,997)(793,996)(794,995)(795,994)(796,993)(797,992)(798,991)(799,990)(800,989)(801,988)(802,987)(803,986)(804,985)(805,984)(806,983)(807,982)(808,981)(809,980)(810,979)(811,978)(812,977)(813,976)(814,975)(815,974)(816,973)(817,972)(818,971)(819,970)(820,969)(821,968)(822,967)(823,966)(824,965)(825,964)(826,963)(827,962)(828,961)(829,960)(830,959)(831,958)(832,957)(833,956)(834,955)(835,954)(836,953)(837,952)(838,951)(839,950)(840,949)(841,948)(842,947)(843,946)(844,945)(845,944)(846,943)(847,942)(848,941)(849,940)(850,939)(851,938)(852,937)(853,936)(854,935)(855,934)(856,933)(857,932)(858,931)(859,930)(860,929)(861,928)(862,927)(863,926)(864,925)(865,924)(866,923)(867,922)(868,921)(869,920)(870,919)(871,918)(872,917)(873,916)(874,915)(875,914)(876,913)(877,912)(878,911)(879,910)(880,909)(881,908)(882,907)(883,906)(884,905)(885,904)(886,903)(887,902)(888,901)(889,900)(890,899)(891,898)(892,897)(893,896)(894,895)
Conjugacy classes & character table
5334 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21324, 18);
Finite Group Databasebeta