← Prev (#36370795) Next (#36370797) →
Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1854 points:
(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854);(4,5)(7,1854)(8,1853)(9,1852)(10,1851)(11,1850)(12,1849)(13,1848)(14,1847)(15,1846)(16,1845)(17,1844)(18,1843)(19,1842)(20,1841)(21,1840)(22,1839)(23,1838)(24,1837)(25,1836)(26,1835)(27,1834)(28,1833)(29,1832)(30,1831)(31,1830)(32,1829)(33,1828)(34,1827)(35,1826)(36,1825)(37,1824)(38,1823)(39,1822)(40,1821)(41,1820)(42,1819)(43,1818)(44,1817)(45,1816)(46,1815)(47,1814)(48,1813)(49,1812)(50,1811)(51,1810)(52,1809)(53,1808)(54,1807)(55,1806)(56,1805)(57,1804)(58,1803)(59,1802)(60,1801)(61,1800)(62,1799)(63,1798)(64,1797)(65,1796)(66,1795)(67,1794)(68,1793)(69,1792)(70,1791)(71,1790)(72,1789)(73,1788)(74,1787)(75,1786)(76,1785)(77,1784)(78,1783)(79,1782)(80,1781)(81,1780)(82,1779)(83,1778)(84,1777)(85,1776)(86,1775)(87,1774)(88,1773)(89,1772)(90,1771)(91,1770)(92,1769)(93,1768)(94,1767)(95,1766)(96,1765)(97,1764)(98,1763)(99,1762)(100,1761)(101,1760)(102,1759)(103,1758)(104,1757)(105,1756)(106,1755)(107,1754)(108,1753)(109,1752)(110,1751)(111,1750)(112,1749)(113,1748)(114,1747)(115,1746)(116,1745)(117,1744)(118,1743)(119,1742)(120,1741)(121,1740)(122,1739)(123,1738)(124,1737)(125,1736)(126,1735)(127,1734)(128,1733)(129,1732)(130,1731)(131,1730)(132,1729)(133,1728)(134,1727)(135,1726)(136,1725)(137,1724)(138,1723)(139,1722)(140,1721)(141,1720)(142,1719)(143,1718)(144,1717)(145,1716)(146,1715)(147,1714)(148,1713)(149,1712)(150,1711)(151,1710)(152,1709)(153,1708)(154,1707)(155,1706)(156,1705)(157,1704)(158,1703)(159,1702)(160,1701)(161,1700)(162,1699)(163,1698)(164,1697)(165,1696)(166,1695)(167,1694)(168,1693)(169,1692)(170,1691)(171,1690)(172,1689)(173,1688)(174,1687)(175,1686)(176,1685)(177,1684)(178,1683)(179,1682)(180,1681)(181,1680)(182,1679)(183,1678)(184,1677)(185,1676)(186,1675)(187,1674)(188,1673)(189,1672)(190,1671)(191,1670)(192,1669)(193,1668)(194,1667)(195,1666)(196,1665)(197,1664)(198,1663)(199,1662)(200,1661)(201,1660)(202,1659)(203,1658)(204,1657)(205,1656)(206,1655)(207,1654)(208,1653)(209,1652)(210,1651)(211,1650)(212,1649)(213,1648)(214,1647)(215,1646)(216,1645)(217,1644)(218,1643)(219,1642)(220,1641)(221,1640)(222,1639)(223,1638)(224,1637)(225,1636)(226,1635)(227,1634)(228,1633)(229,1632)(230,1631)(231,1630)(232,1629)(233,1628)(234,1627)(235,1626)(236,1625)(237,1624)(238,1623)(239,1622)(240,1621)(241,1620)(242,1619)(243,1618)(244,1617)(245,1616)(246,1615)(247,1614)(248,1613)(249,1612)(250,1611)(251,1610)(252,1609)(253,1608)(254,1607)(255,1606)(256,1605)(257,1604)(258,1603)(259,1602)(260,1601)(261,1600)(262,1599)(263,1598)(264,1597)(265,1596)(266,1595)(267,1594)(268,1593)(269,1592)(270,1591)(271,1590)(272,1589)(273,1588)(274,1587)(275,1586)(276,1585)(277,1584)(278,1583)(279,1582)(280,1581)(281,1580)(282,1579)(283,1578)(284,1577)(285,1576)(286,1575)(287,1574)(288,1573)(289,1572)(290,1571)(291,1570)(292,1569)(293,1568)(294,1567)(295,1566)(296,1565)(297,1564)(298,1563)(299,1562)(300,1561)(301,1560)(302,1559)(303,1558)(304,1557)(305,1556)(306,1555)(307,1554)(308,1553)(309,1552)(310,1551)(311,1550)(312,1549)(313,1548)(314,1547)(315,1546)(316,1545)(317,1544)(318,1543)(319,1542)(320,1541)(321,1540)(322,1539)(323,1538)(324,1537)(325,1536)(326,1535)(327,1534)(328,1533)(329,1532)(330,1531)(331,1530)(332,1529)(333,1528)(334,1527)(335,1526)(336,1525)(337,1524)(338,1523)(339,1522)(340,1521)(341,1520)(342,1519)(343,1518)(344,1517)(345,1516)(346,1515)(347,1514)(348,1513)(349,1512)(350,1511)(351,1510)(352,1509)(353,1508)(354,1507)(355,1506)(356,1505)(357,1504)(358,1503)(359,1502)(360,1501)(361,1500)(362,1499)(363,1498)(364,1497)(365,1496)(366,1495)(367,1494)(368,1493)(369,1492)(370,1491)(371,1490)(372,1489)(373,1488)(374,1487)(375,1486)(376,1485)(377,1484)(378,1483)(379,1482)(380,1481)(381,1480)(382,1479)(383,1478)(384,1477)(385,1476)(386,1475)(387,1474)(388,1473)(389,1472)(390,1471)(391,1470)(392,1469)(393,1468)(394,1467)(395,1466)(396,1465)(397,1464)(398,1463)(399,1462)(400,1461)(401,1460)(402,1459)(403,1458)(404,1457)(405,1456)(406,1455)(407,1454)(408,1453)(409,1452)(410,1451)(411,1450)(412,1449)(413,1448)(414,1447)(415,1446)(416,1445)(417,1444)(418,1443)(419,1442)(420,1441)(421,1440)(422,1439)(423,1438)(424,1437)(425,1436)(426,1435)(427,1434)(428,1433)(429,1432)(430,1431)(431,1430)(432,1429)(433,1428)(434,1427)(435,1426)(436,1425)(437,1424)(438,1423)(439,1422)(440,1421)(441,1420)(442,1419)(443,1418)(444,1417)(445,1416)(446,1415)(447,1414)(448,1413)(449,1412)(450,1411)(451,1410)(452,1409)(453,1408)(454,1407)(455,1406)(456,1405)(457,1404)(458,1403)(459,1402)(460,1401)(461,1400)(462,1399)(463,1398)(464,1397)(465,1396)(466,1395)(467,1394)(468,1393)(469,1392)(470,1391)(471,1390)(472,1389)(473,1388)(474,1387)(475,1386)(476,1385)(477,1384)(478,1383)(479,1382)(480,1381)(481,1380)(482,1379)(483,1378)(484,1377)(485,1376)(486,1375)(487,1374)(488,1373)(489,1372)(490,1371)(491,1370)(492,1369)(493,1368)(494,1367)(495,1366)(496,1365)(497,1364)(498,1363)(499,1362)(500,1361)(501,1360)(502,1359)(503,1358)(504,1357)(505,1356)(506,1355)(507,1354)(508,1353)(509,1352)(510,1351)(511,1350)(512,1349)(513,1348)(514,1347)(515,1346)(516,1345)(517,1344)(518,1343)(519,1342)(520,1341)(521,1340)(522,1339)(523,1338)(524,1337)(525,1336)(526,1335)(527,1334)(528,1333)(529,1332)(530,1331)(531,1330)(532,1329)(533,1328)(534,1327)(535,1326)(536,1325)(537,1324)(538,1323)(539,1322)(540,1321)(541,1320)(542,1319)(543,1318)(544,1317)(545,1316)(546,1315)(547,1314)(548,1313)(549,1312)(550,1311)(551,1310)(552,1309)(553,1308)(554,1307)(555,1306)(556,1305)(557,1304)(558,1303)(559,1302)(560,1301)(561,1300)(562,1299)(563,1298)(564,1297)(565,1296)(566,1295)(567,1294)(568,1293)(569,1292)(570,1291)(571,1290)(572,1289)(573,1288)(574,1287)(575,1286)(576,1285)(577,1284)(578,1283)(579,1282)(580,1281)(581,1280)(582,1279)(583,1278)(584,1277)(585,1276)(586,1275)(587,1274)(588,1273)(589,1272)(590,1271)(591,1270)(592,1269)(593,1268)(594,1267)(595,1266)(596,1265)(597,1264)(598,1263)(599,1262)(600,1261)(601,1260)(602,1259)(603,1258)(604,1257)(605,1256)(606,1255)(607,1254)(608,1253)(609,1252)(610,1251)(611,1250)(612,1249)(613,1248)(614,1247)(615,1246)(616,1245)(617,1244)(618,1243)(619,1242)(620,1241)(621,1240)(622,1239)(623,1238)(624,1237)(625,1236)(626,1235)(627,1234)(628,1233)(629,1232)(630,1231)(631,1230)(632,1229)(633,1228)(634,1227)(635,1226)(636,1225)(637,1224)(638,1223)(639,1222)(640,1221)(641,1220)(642,1219)(643,1218)(644,1217)(645,1216)(646,1215)(647,1214)(648,1213)(649,1212)(650,1211)(651,1210)(652,1209)(653,1208)(654,1207)(655,1206)(656,1205)(657,1204)(658,1203)(659,1202)(660,1201)(661,1200)(662,1199)(663,1198)(664,1197)(665,1196)(666,1195)(667,1194)(668,1193)(669,1192)(670,1191)(671,1190)(672,1189)(673,1188)(674,1187)(675,1186)(676,1185)(677,1184)(678,1183)(679,1182)(680,1181)(681,1180)(682,1179)(683,1178)(684,1177)(685,1176)(686,1175)(687,1174)(688,1173)(689,1172)(690,1171)(691,1170)(692,1169)(693,1168)(694,1167)(695,1166)(696,1165)(697,1164)(698,1163)(699,1162)(700,1161)(701,1160)(702,1159)(703,1158)(704,1157)(705,1156)(706,1155)(707,1154)(708,1153)(709,1152)(710,1151)(711,1150)(712,1149)(713,1148)(714,1147)(715,1146)(716,1145)(717,1144)(718,1143)(719,1142)(720,1141)(721,1140)(722,1139)(723,1138)(724,1137)(725,1136)(726,1135)(727,1134)(728,1133)(729,1132)(730,1131)(731,1130)(732,1129)(733,1128)(734,1127)(735,1126)(736,1125)(737,1124)(738,1123)(739,1122)(740,1121)(741,1120)(742,1119)(743,1118)(744,1117)(745,1116)(746,1115)(747,1114)(748,1113)(749,1112)(750,1111)(751,1110)(752,1109)(753,1108)(754,1107)(755,1106)(756,1105)(757,1104)(758,1103)(759,1102)(760,1101)(761,1100)(762,1099)(763,1098)(764,1097)(765,1096)(766,1095)(767,1094)(768,1093)(769,1092)(770,1091)(771,1090)(772,1089)(773,1088)(774,1087)(775,1086)(776,1085)(777,1084)(778,1083)(779,1082)(780,1081)(781,1080)(782,1079)(783,1078)(784,1077)(785,1076)(786,1075)(787,1074)(788,1073)(789,1072)(790,1071)(791,1070)(792,1069)(793,1068)(794,1067)(795,1066)(796,1065)(797,1064)(798,1063)(799,1062)(800,1061)(801,1060)(802,1059)(803,1058)(804,1057)(805,1056)(806,1055)(807,1054)(808,1053)(809,1052)(810,1051)(811,1050)(812,1049)(813,1048)(814,1047)(815,1046)(816,1045)(817,1044)(818,1043)(819,1042)(820,1041)(821,1040)(822,1039)(823,1038)(824,1037)(825,1036)(826,1035)(827,1034)(828,1033)(829,1032)(830,1031)(831,1030)(832,1029)(833,1028)(834,1027)(835,1026)(836,1025)(837,1024)(838,1023)(839,1022)(840,1021)(841,1020)(842,1019)(843,1018)(844,1017)(845,1016)(846,1015)(847,1014)(848,1013)(849,1012)(850,1011)(851,1010)(852,1009)(853,1008)(854,1007)(855,1006)(856,1005)(857,1004)(858,1003)(859,1002)(860,1001)(861,1000)(862,999)(863,998)(864,997)(865,996)(866,995)(867,994)(868,993)(869,992)(870,991)(871,990)(872,989)(873,988)(874,987)(875,986)(876,985)(877,984)(878,983)(879,982)(880,981)(881,980)(882,979)(883,978)(884,977)(885,976)(886,975)(887,974)(888,973)(889,972)(890,971)(891,970)(892,969)(893,968)(894,967)(895,966)(896,965)(897,964)(898,963)(899,962)(900,961)(901,960)(902,959)(903,958)(904,957)(905,956)(906,955)(907,954)(908,953)(909,952)(910,951)(911,950)(912,949)(913,948)(914,947)(915,946)(916,945)(917,944)(918,943)(919,942)(920,941)(921,940)(922,939)(923,938)(924,937)(925,936)(926,935)(927,934)(928,933)(929,932)(930,931)
Conjugacy classes & character table
5550 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22188, 15);
Finite Group Databasebeta