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D10532 #35231024
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2637 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,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07,1836)(808,1835)(809,1834)(810,1833)(811,1832)(812,1831)(813,1830)(814,1829)(815,1828)(816,1827)(817,1826)(818,1825)(819,1824)(820,1823)(821,1822)(822,1821)(823,1820)(824,1819)(825,1818)(826,1817)(827,1816)(828,1815)(829,1814)(830,1813)(831,1812)(832,1811)(833,1810)(834,1809)(835,1808)(836,1807)(837,1806)(838,1805)(839,1804)(840,1803)(841,1802)(842,1801)(843,1800)(844,1799)(845,1798)(846,1797)(847,1796)(848,1795)(849,1794)(850,1793)(851,1792)(852,1791)(853,1790)(854,1789)(855,1788)(856,1787)(857,1786)(858,1785)(859,1784)(860,1783)(861,1782)(862,1781)(863,1780)(864,1779)(865,1778)(866,1777)(867,1776)(868,1775)(869,1774)(870,1773)(871,1772)(872,1771)(873,1770)(874,1769)(875,1768)(876,1767)(877,1766)(878,1765)(879,1764)(880,1763)(881,1762)(882,1761)(883,1760)(884,1759)(885,1758)(886,1757)(887,1756)(888,1755)(889,1754)(890,1753)(891,1752)(892,1751)(893,1750)(894,1749)(895,1748)(896,1747)(897,1746)(898,1745)(899,1744)(900,1743)(901,1742)(902,1741)(903,1740)(904,1739)(905,1738)(906,1737)(907,1736)(908,1735)(909,1734)(910,1733)(911,1732)(912,1731)(913,1730)(914,1729)(915,1728)(916,1727)(917,1726)(918,1725)(919,1724)(920,1723)(921,1722)(922,1721)(923,1720)(924,1719)(925,1718)(926,1717)(927,1716)(928,1715)(929,1714)(930,1713)(931,1712)(932,1711)(933,1710)(934,1709)(935,1708)(936,1707)(937,1706)(938,1705)(939,1704)(940,1703)(941,1702)(942,1701)(943,1700)(944,1699)(945,1698)(946,1697)(947,1696)(948,1695)(949,1694)(950,1693)(951,1692)(952,1691)(953,1690)(954,1689)(955,1688)(956,1687)(957,1686)(958,1685)(959,1684)(960,1683)(961,1682)(962,1681)(963,1680)(964,1679)(965,1678)(966,1677)(967,1676)(968,1675)(969,1674)(970,1673)(971,1672)(972,1671)(973,1670)(974,1669)(975,1668)(976,1667)(977,1666)(978,1665)(979,1664)(980,1663)(981,1662)(982,1661)(983,1660)(984,1659)(985,1658)(986,1657)(987,1656)(988,1655)(989,1654)(990,1653)(991,1652)(992,1651)(993,1650)(994,1649)(995,1648)(996,1647)(997,1646)(998,1645)(999,1644)(1000,1643)(1001,1642)(1002,1641)(1003,1640)(1004,1639)(1005,1638)(1006,1637)(1007,1636)(1008,1635)(1009,1634)(1010,1633)(1011,1632)(1012,1631)(1013,1630)(1014,1629)(1015,1628)(1016,1627)(1017,1626)(1018,1625)(1019,1624)(1020,1623)(1021,1622)(1022,1621)(1023,1620)(1024,1619)(1025,1618)(1026,1617)(1027,1616)(1028,1615)(1029,1614)(1030,1613)(1031,1612)(1032,1611)(1033,1610)(1034,1609)(1035,1608)(1036,1607)(1037,1606)(1038,1605)(1039,1604)(1040,1603)(1041,1602)(1042,1601)(1043,1600)(1044,1599)(1045,1598)(1046,1597)(1047,1596)(1048,1595)(1049,1594)(1050,1593)(1051,1592)(1052,1591)(1053,1590)(1054,1589)(1055,1588)(1056,1587)(1057,1586)(1058,1585)(1059,1584)(1060,1583)(1061,1582)(1062,1581)(1063,1580)(1064,1579)(1065,1578)(1066,1577)(1067,1576)(1068,1575)(1069,1574)(1070,1573)(1071,1572)(1072,1571)(1073,1570)(1074,1569)(1075,1568)(1076,1567)(1077,1566)(1078,1565)(1079,1564)(1080,1563)(1081,1562)(1082,1561)(1083,1560)(1084,1559)(1085,1558)(1086,1557)(1087,1556)(1088,1555)(1089,1554)(1090,1553)(1091,1552)(1092,1551)(1093,1550)(1094,1549)(1095,1548)(1096,1547)(1097,1546)(1098,1545)(1099,1544)(1100,1543)(1101,1542)(1102,1541)(1103,1540)(1104,1539)(1105,1538)(1106,1537)(1107,1536)(1108,1535)(1109,1534)(1110,1533)(1111,1532)(1112,1531)(1113,1530)(1114,1529)(1115,1528)(1116,1527)(1117,1526)(1118,1525)(1119,1524)(1120,1523)(1121,1522)(1122,1521)(1123,1520)(1124,1519)(1125,1518)(1126,1517)(1127,1516)(1128,1515)(1129,1514)(1130,1513)(1131,1512)(1132,1511)(1133,1510)(1134,1509)(1135,1508)(1136,1507)(1137,1506)(1138,1505)(1139,1504)(1140,1503)(1141,1502)(1142,1501)(1143,1500)(1144,1499)(1145,1498)(1146,1497)(1147,1496)(1148,1495)(1149,1494)(1150,1493)(1151,1492)(1152,1491)(1153,1490)(1154,1489)(1155,1488)(1156,1487)(1157,1486)(1158,1485)(1159,1484)(1160,1483)(1161,1482)(1162,1481)(1163,1480)(1164,1479)(1165,1478)(1166,1477)(1167,1476)(1168,1475)(1169,1474)(1170,1473)(1171,1472)(1172,1471)(1173,1470)(1174,1469)(1175,1468)(1176,1467)(1177,1466)(1178,1465)(1179,1464)(1180,1463)(1181,1462)(1182,1461)(1183,1460)(1184,1459)(1185,1458)(1186,1457)(1187,1456)(1188,1455)(1189,1454)(1190,1453)(1191,1452)(1192,1451)(1193,1450)(1194,1449)(1195,1448)(1196,1447)(1197,1446)(1198,1445)(1199,1444)(1200,1443)(1201,1442)(1202,1441)(1203,1440)(1204,1439)(1205,1438)(1206,1437)(1207,1436)(1208,1435)(1209,1434)(1210,1433)(1211,1432)(1212,1431)(1213,1430)(1214,1429)(1215,1428)(1216,1427)(1217,1426)(1218,1425)(1219,1424)(1220,1423)(1221,1422)(1222,1421)(1223,1420)(1224,1419)(1225,1418)(1226,1417)(1227,1416)(1228,1415)(1229,1414)(1230,1413)(1231,1412)(1232,1411)(1233,1410)(1234,1409)(1235,1408)(1236,1407)(1237,1406)(1238,1405)(1239,1404)(1240,1403)(1241,1402)(1242,1401)(1243,1400)(1244,1399)(1245,1398)(1246,1397)(1247,1396)(1248,1395)(1249,1394)(1250,1393)(1251,1392)(1252,1391)(1253,1390)(1254,1389)(1255,1388)(1256,1387)(1257,1386)(1258,1385)(1259,1384)(1260,1383)(1261,1382)(1262,1381)(1263,1380)(1264,1379)(1265,1378)(1266,1377)(1267,1376)(1268,1375)(1269,1374)(1270,1373)(1271,1372)(1272,1371)(1273,1370)(1274,1369)(1275,1368)(1276,1367)(1277,1366)(1278,1365)(1279,1364)(1280,1363)(1281,1362)(1282,1361)(1283,1360)(1284,1359)(1285,1358)(1286,1357)(1287,1356)(1288,1355)(1289,1354)(1290,1353)(1291,1352)(1292,1351)(1293,1350)(1294,1349)(1295,1348)(1296,1347)(1297,1346)(1298,1345)(1299,1344)(1300,1343)(1301,1342)(1302,1341)(1303,1340)(1304,1339)(1305,1338)(1306,1337)(1307,1336)(1308,1335)(1309,1334)(1310,1333)(1311,1332)(1312,1331)(1313,1330)(1314,1329)(1315,1328)(1316,1327)(1317,1326)(1318,1325)(1319,1324)(1320,1323)(1321,1322)
Polycyclic presentation:
2^3,2633|b^a=bc,d^a=d^2632,d^b=d^2632
Conjugacy classes & character table
5269 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21064, 10);
Finite Group Databasebeta