← Prev (#46797884) Next (#46797886) →
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1876 points:
(2,3)(5,6,8)(7,10,15)(9,13,12)(11,17,25)(14,20,22)(16,23,19)(18,27,38)(21,30,35)(24,33,32)(26,36,29)(28,40,54)(31,43,51)(34,46,48)(37,49,45)(39,52,42)(41,56,73)(44,59,70)(47,62,67)(50,65,64)(53,68,61)(55,71,58)(57,75,95)(60,78,92)(63,81,89)(66,84,86)(69,87,83)(72,90,80)(74,93,77)(76,97,120)(79,100,117)(82,103,114)(85,106,111)(88,109,108)(91,112,105)(94,115,102)(96,118,99)(98,122,148)(101,125,145)(104,128,142)(107,131,139)(110,134,136)(113,137,133)(116,140,130)(119,143,127)(121,146,124)(123,150,179)(126,153,176)(129,156,173)(132,159,170)(135,162,167)(138,165,164)(141,168,161)(144,171,158)(147,174,155)(149,177,152)(151,181,213)(154,184,210)(157,187,207)(160,190,204)(163,193,201)(166,196,198)(169,199,195)(172,202,192)(175,205,189)(178,208,186)(180,211,183)(182,215,250)(185,218,247)(188,221,244)(191,224,241)(194,227,238)(197,230,235)(200,233,232)(203,236,229)(206,239,226)(209,242,223)(212,245,220)(214,248,217)(216,252,290)(219,255,287)(222,258,284)(225,261,281)(228,264,278)(231,267,275)(234,270,272)(237,273,269)(240,276,266)(243,279,263)(246,282,260)(249,285,257)(251,288,254)(253,292,333)(256,295,330)(259,298,327)(262,301,324)(265,304,321)(268,307,318)(271,310,315)(274,313,312)(277,316,309)(280,319,306)(283,322,303)(286,325,300)(289,328,297)(291,331,294)(293,335,379)(296,338,376)(299,341,373)(302,344,370)(305,347,367)(308,350,364)(311,353,361)(314,356,358)(317,359,355)(320,362,352)(323,365,349)(326,368,346)(329,371,343)(332,374,340)(334,377,337)(336,381,428)(339,384,425)(342,387,422)(345,390,419)(348,393,416)(351,396,413)(354,399,410)(357,402,407)(360,405,404)(363,408,401)(366,411,398)(369,414,395)(372,417,392)(375,420,389)(378,423,386)(380,426,383)(382,430,480)(385,433,477)(388,436,474)(391,439,471)(394,442,468)(397,445,465)(400,448,462)(403,451,459)(406,454,456)(409,457,453)(412,460,450)(415,463,447)(418,466,444)(421,469,441)(424,472,438)(427,475,435)(429,478,432)(431,482,535)(434,485,532)(437,488,529)(440,491,526)(443,494,523)(446,497,520)(449,500,517)(452,503,514)(455,506,511)(458,509,508)(461,512,505)(464,515,502)(467,518,499)(470,521,496)(473,524,493)(476,527,490)(479,530,487)(481,533,484)(483,537,593)(486,540,590)(489,543,587)(492,546,584)(495,549,581)(498,552,578)(501,555,575)(504,558,572)(507,561,569)(510,564,566)(513,567,563)(516,570,560)(519,573,557)(522,576,554)(525,579,551)(528,582,548)(531,585,545)(534,588,542)(536,591,539)(538,595,654)(541,598,651)(544,601,648)(547,604,645)(550,607,642)(553,610,639)(556,613,636)(559,616,633)(562,619,630)(565,622,627)(568,625,624)(571,628,621)(574,631,618)(577,634,615)(580,637,612)(583,640,609)(586,643,606)(589,646,603)(592,649,600)(594,652,597)(596,656,718)(599,659,715)(602,662,712)(605,665,709)(608,668,706)(611,671,703)(614,674,700)(617,677,697)(620,680,694)(623,683,691)(626,686,688)(629,689,685)(632,692,682)(635,695,679)(638,698,676)(641,701,673)(644,704,670)(647,707,667)(650,710,664)(653,713,661)(655,716,658)(657,720,785)(660,723,782)(663,726,779)(666,729,776)(669,732,773)(672,735,770)(675,738,767)(678,741,764)(681,744,761)(684,747,758)(687,750,755)(690,753,752)(693,756,749)(696,759,746)(699,762,743)(702,765,740)(705,768,737)(708,771,734)(711,774,731)(714,777,728)(717,780,725)(719,783,722)(721,787,855)(724,790,852)(727,793,849)(730,796,846)(733,799,843)(736,802,840)(739,805,837)(742,808,834)(745,811,831)(748,814,828)(751,817,825)(754,820,822)(757,823,819)(760,826,816)(763,829,813)(766,832,810)(769,835,807)(772,838,804)(775,841,801)(778,844,798)(781,847,795)(784,850,792)(786,853,789)(788,857,928)(791,860,925)(794,863,922)(797,866,919)(800,869,916)(803,872,913)(806,875,910)(809,878,907)(812,881,904)(815,884,901)(818,887,898)(821,890,895)(824,893,892)(827,896,889)(830,899,886)(833,902,883)(836,905,880)(839,908,877)(842,911,874)(845,914,871)(848,917,868)(851,920,865)(854,923,862)(856,926,859)(858,930,1004)(861,933,1001)(864,936,998)(867,939,995)(870,942,992)(873,945,989)(876,948,986)(879,951,983)(882,954,980)(885,957,977)(888,960,974)(891,963,971)(894,966,968)(897,969,965)(900,972,962)(903,975,959)(906,978,956)(909,981,953)(912,984,950)(915,987,947)(918,990,944)(921,993,941)(924,996,938)(927,999,935)(929,1002,932)(931,1006,1083)(934,1009,1080)(937,1012,1077)(940,1015,1074)(943,1018,1071)(946,1021,1068)(949,1024,1065)(952,1027,1062)(955,1030,1059)(958,1033,1056)(961,1036,1053)(964,1039,1050)(967,1042,1047)(970,1045,1044)(973,1048,1041)(976,1051,1038)(979,1054,1035)(982,1057,1032)(985,1060,1029)(988,1063,1026)(991,1066,1023)(994,1069,1020)(997,1072,1017)(1000,1075,1014)(1003,1078,1011)(1005,1081,1008)(1007,1085,1151)(1010,1087,1161)(1013,1090,1158)(1016,1093,1155)(1019,1096,1152)(1022,1099,1149)(1025,1102,1146)(1028,1105,1143)(1031,1108,1140)(1034,1111,1137)(1037,1114,1134)(1040,1117,1131)(1043,1120,1128)(1046,1123,1125)(1049,1126,1122)(1052,1129,1119)(1055,1132,1116)(1058,1135,1113)(1061,1138,1110)(1064,1141,1107)(1067,1144,1104)(1070,1147,1101)(1073,1150,1098)(1076,1153,1095)(1079,1156,1092)(1082,1159,1089)(1084,1162,1086)(1088,1166,1227)(1091,1168,1237)(1094,1171,1234)(1097,1174,1231)(1100,1177,1228)(1103,1179,1226)(1106,1182,1223)(1109,1185,1220)(1112,1188,1217)(1115,1191,1214)(1118,1194,1211)(1121,1197,1208)(1124,1200,1205)(1127,1203,1202)(1130,1206,1199)(1133,1209,1196)(1136,1212,1193)(1139,1215,1190)(1142,1218,1187)(1145,1221,1184)(1148,1224,1181)(1154,1229,1176)(1157,1232,1173)(1160,1235,1170)(1163,1238,1167)(1164,1230,1165)(1169,1242,1299)(1172,1244,1307)(1175,1247,1304)(1178,1250,1301)(1180,1252,1300)(1183,1254,1298)(1186,1257,1295)(1189,1260,1292)(1192,1263,1289)(1195,1266,1286)(1198,1269,1283)(1201,1272,1280)(1204,1275,1277)(1207,1278,1274)(1210,1281,1271)(1213,1284,1268)(1216,1287,1265)(1219,1290,1262)(1222,1293,1259)(1225,1296,1256)(1233,1302,1249)(1236,1305,1246)(1239,1308,1243)(1240,1303,1241)(1245,1312,1365)(1248,1314,1371)(1251,1317,1368)(1253,1319,1367)(1255,1321,1366)(1258,1323,1364)(1261,1326,1361)(1264,1329,1358)(1267,1332,1355)(1270,1335,1352)(1273,1338,1349)(1276,1341,1346)(1279,1344,1343)(1282,1347,1340)(1285,1350,1337)(1288,1353,1334)(1291,1356,1331)(1294,1359,1328)(1297,1362,1325)(1306,1369,1316)(1309,1372,1313)(1310,1370,1311)(1315,1376,1425)(1318,1378,1429)(1320,1380,1428)(1322,1382,1427)(1324,1384,1426)(1327,1386,1424)(1330,1389,1421)(1333,1392,1418)(1336,1395,1415)(1339,1398,1412)(1342,1401,1409)(1345,1404,1406)(1348,1407,1403)(1351,1410,1400)(1354,1413,1397)(1357,1416,1394)(1360,1419,1391)(1363,1422,1388)(1373,1430,1377)(1374,1431,1375)(1379,1434,1479)(1381,1435,1483)(1383,1437,1482)(1385,1439,1481)(1387,1441,1480)(1390,1443,1478)(1393,1446,1475)(1396,1449,1472)(1399,1452,1469)(1402,1455,1466)(1405,1458,1463)(1408,1461,1460)(1411,1464,1457)(1414,1467,1454)(1417,1470,1451)(1420,1473,1448)(1423,1476,1445)(1432,1484,1433)(1436,1485,1527)(1438,1486,1531)(1440,1488,1530)(1442,1490,1529)(1444,1492,1528)(1447,1494,1526)(1450,1497,1523)(1453,1500,1520)(1456,1503,1517)(1459,1506,1514)(1462,1509,1511)(1465,1512,1508)(1468,1515,1505)(1471,1518,1502)(1474,1521,1499)(1477,1524,1496)(1487,1532,1571)(1489,1533,1575)(1491,1535,1574)(1493,1537,1573)(1495,1539,1572)(1498,1541,1570)(1501,1544,1567)(1504,1547,1564)(1507,1550,1561)(1510,1553,1558)(1513,1556,1555)(1516,1559,1552)(1519,1562,1549)(1522,1565,1546)(1525,1568,1543)(1534,1576,1612)(1536,1577,1616)(1538,1579,1615)(1540,1581,1614)(1542,1583,1613)(1545,1585,1611)(1548,1588,1608)(1551,1591,1605)(1554,1594,1602)(1557,1597,1599)(1560,1600,1596)(1563,1603,1593)(1566,1606,1590)(1569,1609,1587)(1578,1617,1650)(1580,1618,1654)(1582,1620,1653)(1584,1622,1652)(1586,1624,1651)(1589,1626,1649)(1592,1629,1646)(1595,1632,1643)(1598,1635,1640)(1601,1638,1637)(1604,1641,1634)(1607,1644,1631)(1610,1647,1628)(1619,1655,1685)(1621,1656,1689)(1623,1658,1688)(1625,1660,1687)(1627,1662,1686)(1630,1664,1684)(1633,1667,1681)(1636,1670,1678)(1639,1673,1675)(1642,1676,1672)(1645,1679,1669)(1648,1682,1666)(1657,1690,1717)(1659,1691,1721)(1661,1693,1720)(1663,1695,1719)(1665,1697,1718)(1668,1699,1716)(1671,1702,1713)(1674,1705,1710)(1677,1708,1707)(1680,1711,1704)(1683,1714,1701)(1692,1722,1746)(1694,1723,1750)(1696,1725,1749)(1698,1727,1748)(1700,1729,1747)(1703,1731,1745)(1706,1734,1742)(1709,1737,1739)(1712,1740,1736)(1715,1743,1733)(1724,1751,1772)(1726,1752,1776)(1728,1754,1775)(1730,1756,1774)(1732,1758,1773)(1735,1760,1771)(1738,1763,1768)(1741,1766,1765)(1744,1769,1762)(1753,1777,1795)(1755,1778,1799)(1757,1780,1798)(1759,1782,1797)(1761,1784,1796)(1764,1786,1794)(1767,1789,1791)(1770,1792,1788)(1779,1800,1815)(1781,1801,1819)(1783,1803,1818)(1785,1805,1817)(1787,1807,1816)(1790,1809,1814)(1793,1812,1811)(1802,1820,1832)(1804,1821,1836)(1806,1823,1835)(1808,1825,1834)(1810,1827,1833)(1813,1829,1831)(1822,1837,1846)(1824,1838,1850)(1826,1840,1849)(1828,1842,1848)(1830,1844,1847)(1839,1851,1858)(1841,1852,1861)(1843,1854,1860)(1845,1856,1859)(1853,1862,1867)(1855,1863,1869)(1857,1865,1868)(1864,1870,1873)(1866,1871,1874)(1872,1875,1876);(1,2,3)(4,5,7,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,858,931,1007,1069,917,777,649,533,428,477,529,584,642,703,767,834,904,977,1053,1131,1208,1280,1346,1406,1460,1508,1552,1593,1631,1666,1655,1577,1488,1382,1252,1099,942,796,662,540,430,481,534,589,647,708,772,839,909,982,1058,1136,1213,1285,1351,1411,1465,1513,1557,1598,1636,1671,1703,1732,1759,1783,1804,1822,1829,1789,1737,1673,1597,1509,1404,1275,1123,966,820,686,564,454,356,270,196,134,84,46,20,6,9,14,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,861,934,1010,1088,1147,990,844,710,588,478,379,425,474,526,581,639,700,764,831,901,974,1050,1128,1205,1277,1343,1403,1457,1505,1549,1590,1628,1617,1533,1437,1319,1177,1018,866,726,598,482,536,592,650,711,775,842,912,985,1061,1139,1216,1288,1354,1414,1468,1516,1560,1601,1639,1674,1706,1735,1761,1785,1806,1824,1839,1844,1809,1763,1705,1635,1553,1458,1341,1200,1042,890,750,622,506,402,310,230,162,106,62,30,10,16,24,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,794,864,937,1013,1091,1169,1224,1066,914,774,646,530,426,333,376,422,471,523,578,636,697,761,828,898,971,1047,1125,1202,1274,1340,1400,1454,1502,1546,1587,1576,1486,1380,1250,1096,939,793,659,537,594,653,714,778,845,915,988,1064,1142,1219,1291,1357,1417,1471,1519,1563,1604,1642,1677,1709,1738,1764,1787,1808,1826,1841,1853,1856,1827,1786,1734,1670,1594,1506,1401,1272,1120,963,817,683,561,451,353,267,193,131,81,43,17,26,37,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,867,940,1016,1094,1172,1245,1296,1144,987,841,707,585,475,377,290,330,373,419,468,520,575,633,694,758,825,895,968,1044,1122,1199,1271,1337,1397,1451,1499,1543,1532,1435,1317,1174,1015,863,723,595,655,717,781,848,918,991,1067,1145,1222,1294,1360,1420,1474,1522,1566,1607,1645,1680,1712,1741,1767,1790,1810,1828,1843,1855,1864,1865,1842,1807,1760,1702,1632,1550,1455,1338,1197,1039,887,747,619,503,399,307,227,159,103,59,27,39,53,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,870,943,1019,1097,1175,1248,1315,1362,1221,1063,911,771,643,527,423,331,250,287,327,370,416,465,517,572,630,691,755,822,892,965,1041,1119,1196,1268,1334,1394,1448,1496,1485,1378,1247,1093,936,790,656,719,784,851,921,994,1070,1148,1225,1297,1363,1423,1477,1525,1569,1610,1648,1683,1715,1744,1770,1793,1813,1830,1845,1857,1866,1872,1871,1854,1825,1784,1731,1667,1591,1503,1398,1269,1117,960,814,680,558,448,350,264,190,128,78,40,55,72,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,803,873,946,1022,1100,1178,1251,1318,1379,1422,1293,1141,984,838,704,582,472,374,288,213,247,284,324,367,413,462,514,569,627,688,752,819,889,962,1038,1116,1193,1265,1331,1391,1445,1434,1314,1171,1012,860,720,786,854,924,997,1073,1151,1227,1299,1365,1425,1479,1527,1571,1612,1650,1685,1717,1746,1772,1795,1815,1832,1846,1858,1867,1873,1876,1875,1863,1840,1805,1758,1699,1629,1547,1452,1335,1194,1036,884,744,616,500,396,304,224,156,100,56,74,94,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,806,876,949,1025,1103,1180,1253,1320,1381,1436,1476,1359,1218,1060,908,768,640,524,420,328,248,179,210,244,281,321,364,410,459,511,566,624,685,749,816,886,959,1035,1113,1190,1262,1328,1388,1376,1244,1090,933,787,856,927,1000,1076,1154,1230,1083,1161,1237,1307,1371,1429,1483,1531,1575,1616,1654,1689,1721,1750,1776,1799,1819,1836,1850,1861,1869,1874,1870,1852,1823,1782,1729,1664,1588,1500,1395,1266,1114,957,811,677,555,445,347,261,187,125,75,96,119,144,172,203,237,274,314,357,403,452,504,559,617,678,742,809,879,952,1028,1106,1183,1255,1322,1383,1438,1487,1524,1419,1290,1138,981,835,701,579,469,371,285,211,148,176,207,241,278,318,361,407,456,508,563,621,682,746,813,883,956,1032,1110,1187,1259,1325,1312,1168,1009,857,929,1003,1079,1157,1233,1303,1162,1004,1080,1158,1234,1304,1368,1428,1482,1530,1574,1615,1653,1688,1720,1749,1775,1798,1818,1835,1849,1860,1868,1862,1838,1803,1756,1697,1626,1544,1449,1332,1191,1033,881,741,613,497,393,301,221,153,97,121,147,175,206,240,277,317,360,406,455,507,562,620,681,745,812,882,955,1031,1109,1186,1258,1324,1385,1440,1489,1534,1568,1473,1356,1215,1057,905,765,637,521,417,325,245,177,120,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,880,953,1029,1107,1184,1256,1242,1087,930,1005,1082,1160,1236,1306,1370,1238,1081,928,1001,1077,1155,1231,1301,1367,1427,1481,1529,1573,1614,1652,1687,1719,1748,1774,1797,1817,1834,1848,1859,1851,1821,1780,1727,1662,1585,1497,1392,1263,1111,954,808,674,552,442,344,258,184,122,149,178,209,243,280,320,363,409,458,510,565,623,684,748,815,885,958,1034,1112,1189,1261,1327,1387,1442,1491,1536,1578,1609,1521,1416,1287,1135,978,832,698,576,466,368,282,208,146,95,117,142,170,201,235,272,312,355,401,450,502,557,615,676,740,807,877,950,1026,1104,1181,1166,1006,1084,1163,1239,1309,1373,1431,1308,1159,1002,855,925,998,1074,1152,1228,1300,1366,1426,1480,1528,1572,1613,1651,1686,1718,1747,1773,1796,1816,1833,1847,1837,1801,1754,1695,1624,1541,1446,1329,1188,1030,878,738,610,494,390,298,218,150,180,212,246,283,323,366,412,461,513,568,626,687,751,818,888,961,1037,1115,1192,1264,1330,1390,1444,1493,1538,1580,1619,1647,1565,1470,1353,1212,1054,902,762,634,518,414,322,242,174,118,73,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,737,804,874,947,1023,1101,1085,1164,1240,1310,1374,1432,1484,1372,1235,1078,926,785,852,922,995,1071,1149,1226,1298,1364,1424,1478,1526,1570,1611,1649,1684,1716,1745,1771,1794,1814,1831,1820,1778,1725,1660,1583,1494,1389,1260,1108,951,805,671,549,439,341,255,181,214,249,286,326,369,415,464,516,571,629,690,754,821,891,964,1040,1118,1195,1267,1333,1393,1447,1495,1540,1582,1621,1657,1682,1606,1518,1413,1284,1132,975,829,695,573,463,365,279,205,143,93,54,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,670,734,801,871,944,1020,1098,1176,1249,1316,1377,1433,1430,1305,1156,999,853,718,782,849,919,992,1068,1146,1223,1295,1361,1421,1475,1523,1567,1608,1646,1681,1713,1742,1768,1791,1811,1800,1752,1693,1622,1539,1443,1326,1185,1027,875,735,607,491,387,295,215,251,289,329,372,418,467,519,574,632,693,757,824,894,967,1043,1121,1198,1270,1336,1396,1450,1498,1542,1584,1623,1659,1692,1714,1644,1562,1467,1350,1209,1051,899,759,631,515,411,319,239,171,115,71,38,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,667,731,798,868,941,1017,1095,1173,1246,1313,1375,1369,1232,1075,923,783,654,715,779,846,916,989,1065,1143,1220,1292,1358,1418,1472,1520,1564,1605,1643,1678,1710,1739,1765,1788,1777,1723,1658,1581,1492,1386,1257,1105,948,802,668,546,436,338,252,291,332,375,421,470,522,577,635,696,760,827,897,970,1046,1124,1201,1273,1339,1399,1453,1501,1545,1586,1625,1661,1694,1724,1743,1679,1603,1515,1410,1281,1129,972,826,692,570,460,362,276,202,140,90,52,25,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,664,728,795,865,938,1014,1092,1170,1243,1311,1302,1153,996,850,716,593,651,712,776,843,913,986,1062,1140,1217,1289,1355,1415,1469,1517,1561,1602,1640,1675,1707,1736,1762,1751,1691,1620,1537,1441,1323,1182,1024,872,732,604,488,384,292,334,378,424,473,525,580,638,699,763,830,900,973,1049,1127,1204,1276,1342,1402,1456,1504,1548,1589,1627,1663,1696,1726,1753,1769,1711,1641,1559,1464,1347,1206,1048,896,756,628,512,408,316,236,168,112,68,36,15,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,661,725,792,862,935,1011,1089,1167,1241,1229,1072,920,780,652,535,590,648,709,773,840,910,983,1059,1137,1214,1286,1352,1412,1466,1514,1558,1599,1637,1672,1704,1733,1722,1656,1579,1490,1384,1254,1102,945,799,665,543,433,335,380,427,476,528,583,641,702,766,833,903,976,1052,1130,1207,1279,1345,1405,1459,1507,1551,1592,1630,1665,1698,1728,1755,1779,1792,1740,1676,1600,1512,1407,1278,1126,969,823,689,567,457,359,273,199,137,87,49,23,8,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,658,722,789,859,932,1008,1086,1165,1150,993,847,713,591,480,532,587,645,706,770,837,907,980,1056,1134,1211,1283,1349,1409,1463,1511,1555,1596,1634,1669,1701,1690,1618,1535,1439,1321,1179,1021,869,729,601,485,381,429,479,531,586,644,705,769,836,906,979,1055,1133,1210,1282,1348,1408,1462,1510,1554,1595,1633,1668,1700,1730,1757,1781,1802,1812,1766,1708,1638,1556,1461,1344,1203,1045,893,753,625,509,405,313,233,165,109,65,33,13)
Conjugacy classes & character table
1881 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33714, 12);
Finite Group Databasebeta