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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2239 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,93)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,82,80,58,59,57)(51,98,99,72,73,128)(53,96,97,75,71,90)(56,65,95,77,78,91)(60,111,112,83,84,86)(63,117,109,87,88,81)(74,133,134,101,102,169)(76,131,132,104,100,125)(79,94,130,106,107,126)(85,146,147,113,114,121)(89,153,151,118,119,116)(92,158,144,122,123,110)(103,174,175,136,137,216)(105,172,173,139,135,166)(108,129,171,141,142,167)(115,187,188,148,149,162)(120,194,195,154,155,157)(124,200,192,159,160,152)(127,205,185,163,164,145)(138,221,222,177,178,269)(140,219,220,180,176,213)(143,170,218,182,183,214)(150,234,235,189,190,209)(156,241,242,196,197,204)(161,248,246,201,202,199)(165,253,239,206,207,193)(168,258,232,210,211,186)(179,274,275,224,225,328)(181,272,273,227,223,266)(184,217,271,229,230,267)(191,287,288,236,237,262)(198,294,295,243,244,257)(203,301,302,249,250,252)(208,307,299,254,255,247)(212,312,292,259,260,240)(215,317,285,263,264,233)(226,333,334,277,278,393)(228,331,332,280,276,325)(231,270,330,282,283,326)(238,346,347,289,290,321)(245,353,354,296,297,316)(251,360,361,303,304,311)(256,367,365,308,309,306)(261,372,358,313,314,300)(265,377,351,318,319,293)(268,382,344,322,323,286)(279,398,399,336,337,464)(281,396,397,339,335,390)(284,329,395,341,342,391)(291,411,412,348,349,386)(298,418,419,355,356,381)(305,425,426,362,363,376)(310,432,433,368,369,371)(315,438,430,373,374,366)(320,443,423,378,379,359)(324,448,416,383,384,352)(327,453,409,387,388,345)(338,469,470,401,402,541)(340,467,468,404,400,461)(343,394,466,406,407,462)(350,482,483,413,414,457)(357,489,490,420,421,452)(364,496,497,427,428,447)(370,503,504,434,435,442)(375,510,508,439,440,437)(380,515,501,444,445,431)(385,520,494,449,450,424)(389,525,487,454,455,417)(392,530,480,458,459,410)(403,546,547,472,473,624)(405,544,545,475,471,538)(408,465,543,477,478,539)(415,559,560,484,485,534)(422,566,567,491,492,529)(429,573,574,498,499,524)(436,580,581,505,506,519)(441,587,588,511,512,514)(446,593,585,516,517,509)(451,598,578,521,522,502)(456,603,571,526,527,495)(460,608,564,531,532,488)(463,613,557,535,536,481)(474,629,630,549,550,713)(476,627,628,552,548,621)(479,542,626,554,555,622)(486,642,643,561,562,617)(493,649,650,568,569,612)(500,656,657,575,576,607)(507,663,664,582,583,602)(513,670,671,589,590,597)(518,677,675,594,595,592)(523,682,668,599,600,586)(528,687,661,604,605,579)(533,692,654,609,610,572)(537,697,647,614,615,565)(540,702,640,618,619,558)(551,718,719,632,633,808)(553,716,717,635,631,710)(556,625,715,637,638,711)(563,731,732,644,645,706)(570,738,739,651,652,701)(577,745,746,658,659,696)(584,752,753,665,666,691)(591,759,760,672,673,686)(596,766,767,678,679,681)(601,772,764,683,684,676)(606,777,757,688,689,669)(611,782,750,693,694,662)(616,787,743,698,699,655)(620,792,736,703,704,648)(623,797,729,707,708,641)(634,813,814,721,722,909)(636,811,812,724,720,805)(639,714,810,726,727,806)(646,826,827,733,734,801)(653,833,834,740,741,796)(660,840,841,747,748,791)(667,847,848,754,755,786)(674,854,855,761,762,781)(680,861,862,768,769,776)(685,868,866,773,774,771)(690,873,859,778,779,765)(695,878,852,783,784,758)(700,883,845,788,789,751)(705,888,838,793,794,744)(709,893,831,798,799,737)(712,898,824,802,803,730)(723,914,915,816,817,1016)(725,912,913,819,815,906)(728,809,911,821,822,907)(735,927,928,828,829,902)(742,934,935,835,836,897)(749,941,942,842,843,892)(756,948,949,849,850,887)(763,955,956,856,857,882)(770,962,963,863,864,877)(775,969,970,869,870,872)(780,975,967,874,875,867)(785,980,960,879,880,860)(790,985,953,884,885,853)(795,990,946,889,890,846)(800,995,939,894,895,839)(804,1000,932,899,900,832)(807,1005,925,903,904,825)(818,1021,1022,917,918,1129)(820,1019,1020,920,916,1013)(823,910,1018,922,923,1014)(830,1034,1035,929,930,1009)(837,1041,1042,936,937,1004)(844,1048,1049,943,944,999)(851,1055,1056,950,951,994)(858,1062,1063,957,958,989)(865,1069,1070,964,965,984)(871,1076,1077,971,972,979)(876,1083,1081,976,977,974)(881,1088,1074,981,982,968)(886,1093,1067,986,987,961)(891,1098,1060,991,992,954)(896,1103,1053,996,997,947)(901,1108,1046,1001,1002,940)(905,1113,1039,1006,1007,933)(908,1118,1032,1010,1011,926)(919,1134,1135,1024,1025,1248)(921,1132,1133,1027,1023,1126)(924,1017,1131,1029,1030,1127)(931,1147,1148,1036,1037,1122)(938,1154,1155,1043,1044,1117)(945,1161,1162,1050,1051,1112)(952,1168,1169,1057,1058,1107)(959,1175,1176,1064,1065,1102)(966,1182,1183,1071,1072,1097)(973,1189,1190,1078,1079,1092)(978,1196,1197,1084,1085,1087)(983,1202,1194,1089,1090,1082)(988,1207,1187,1094,1095,1075)(993,1212,1180,1099,1100,1068)(998,1217,1173,1104,1105,1061)(1003,1222,1166,1109,1110,1054)(1008,1227,1159,1114,1115,1047)(1012,1232,1152,1119,1120,1040)(1015,1237,1145,1123,1124,1033)(1026,1253,1254,1137,1138,1373)(1028,1251,1252,1140,1136,1245)(1031,1130,1250,1142,1143,1246)(1038,1266,1267,1149,1150,1241)(1045,1273,1274,1156,1157,1236)(1052,1280,1281,1163,1164,12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356,363,369,374,379,384,388,391,393,461,534,612,696,786,882,984,1092,1206,1326,1452,1584,1721,1864,2011,2091,1962,1814,1671,1534,1403,1278,1159,1046,939,838,743,654,571,494,423,358,299,246,195,147,97,47,66,82,67,46,65,92,124,161,203,251,305,364,429,500,577,660,749,844,945,1052,1165,1284,1409,1540,1677,1820,1968,2097,2169,2186,2115,1979,1824,1674,1530,1392,1252,1022,1131,1237,1232,1227,1222,1217,1212,1207,1202,1196,1189,1182,1175,1168,1161,1154,1147,1132,1021,1130,1247,1369,1496,1628,1766,1910,2053,1908,1764,1626,1494,1367,1143,918,1023,1037,1044,1051,1058,1065,1072,1079,1085,1090,1095,1100,1105,1110,1115,1120,1124,1127,1129,1245,1366,1492,1624,1762,1906,2051,2150,2197,2167,2095,1966,1818,1675,1538,1407,1282,1163,1050,943,842,747,658,575,498,427,362,303,249,201,159,122,78,31,48,59,62,64,90,121,157,199,247,300,359,424,495,572,655,744,839,940,1047,1160,1279,1404,1535,1672,1815,1963,2092,2010,1863,1720,1583,1448,1316,1190,1070,956,848,746,650,560,468,334,395,453,448,443,438,432,425,418,411,396,333,394,463,537,616,700,790,886,988,1096,1210,1330,1456,1588,1726,1869,2016,2082,2089,2096,2103,2110,2117,2122,2127,2131,2135,1939,2072,2139,2141,2143,2146,2149,2151,2148,2145,2142,2140,2138,2137,2136,2133,2129,2124,2119,2114,2107,2100,2093,2086,2079,2073,1938,2021,1873,1729,1591,1459,1333,1213,1099,991,889,793,703,618,478,337,400,414,421,428,435,440,445,450,455,459,462,464,538,617,701,791,887,989,1097,1211,1331,1457,1589,1727,1871,2018,2084,1955,1807,1664,1527,1396,1271,1152,1039,932,831,736,647,564,487,416,351,292,239,192,151,112,68,28,43,44,27,42,63,89,120,156,198,245,298,357,422,493,570,653,742,837,938,1045,1158,1277,1402,1533,1670,1813,1961,2090,2164,2120,1986,1831,1681,1537,1399,1267,1133,915,1018,1118,1113,1108,1103,1098,1093,1088,1083,1076,1069,1062,1055,1048,1041,1034,1019,914,1017,1128,1244,1365,1491,1623,1761,1905,2050,1913,1769,1631,1498,1262,1025,1136,1150,1157,1164,1171,1178,1185,1192,1199,1204,1209,1214,1219,1224,1229,1234,1239,1243,1246,1248,1370,1497,1629,1767,1911,2055,2152,2198,2208,2172,2102,1973,1825,1682,1545,1414,1289,1170,1057,950,849,754,665,582,505,434,368,308,254,206,163,107,50,71,84,88,91,93,125,162,204,252,306,366,431,502,579,662,751,846,947,1054,1167,1286,1411,1542,1679,1822,1970,2099,2004,1856,1713,1576,1445,1320,1197,1077,963,855,753,657,567,483,397,275,330,382,377,372,367,360,353,346,331,274,329,392,460,533,611,695,785,881,983,1091,1205,1325,1451,1582,1719,1862,2009,2132,2168,2173,2178,2183,2188,2192,2196,2160,2074,1790,1935,2065,2062,2059,2056,2052,2047,2042,2037,2032,2028,2024,2019,2012,2006,1999,1992,1985,1978,1971,1964,1957,1950,1936,1789,1934,2025,1878,1734,1596,1464,1338,1218,1104,996,894,798,707,555,402,471,485,492,499,506,512,517,522,527,532,536,539,541,621,706,796,892,994,1102,1216,1336,1462,1594,1732,1876,2023,2077,1948,1800,1657,1520,1389,1264,1145,1032,925,824,729,640,557,480,409,344,285,232,185,144,109,80,45,15,26,14,25,40,60,85,115,150,191,238,291,350,415,486,563,646,735,830,931,1038,1151,1270,1395,1526,1663,1806,1954,2083,2125,1993,1838,1688,1544,1406,1274,1148,1020,814,911,1005,1000,995,990,985,980,975,969,962,955,948,941,934,927,912,813,910,1015,1125,1240,1360,1486,1618,1756,1900,2045,1918,1774,1635,1387,1138,1255,1269,1276,1283,1290,1297,1304,1311,1318,1324,1329,1334,1339,1344,1349,1354,1359,1364,1368,1371,1373,1501,1634,1772,1916,2058,2153,2199,2227,2212,2177,2109,1980,1832,1689,1552,1421,1296,1177,1064,957,856,761,672,589,511,439,373,313,259,210,142,73,100,114,119,123,126,128,166,209,257,311,371,437,509,586,669,758,853,954,1061,1174,1293,1418,1549,1686,1829,1977,2106,1997,1849,1706,1569,1438,1313,1194,1081,970,862,760,664,574,490,412,332,222,271,317,312,307,301,294,287,272,221,270,327,389,456,528,606,690,780,876,978,1086,1200,1319,1444,1575,1712,1855,2003,2128,2193,2213,2218,2222,2226,2205,2162,2080,1937,1647,1786,1922,1917,1912,1907,1902,1897,1892,1887,1882,1877,1872,1865,1858,1851,1844,1837,1830,1823,1816,1809,1802,1787,1646,1785,1932,2029,1883,1739,1601,1469,1343,1223,1109,1001,899,802,638,473,548,562,569,576,583,590,595,600,605,610,615,619,622,624,710,801,897,999,1107,1221,1341,1467,1599,1737,1881,2027,1945,1797,1654,1517,1386,1261,1142,1029,922,821,726,637,554,477,406,341,282,229,182,141,106,77,54,35,22,7,6,12,21,34,53,76,105,140,181,228,281,340,405,476,553,636,725,820,921,1028,1141,1260,1385,1516,1653,1796,1944,2076,2000,1845,1695,1551,1413,1281,1155,1035,913,719,810,898,893,888,883,878,873,868,861,854,847,840,833,826,811,718,809,908,1012,1121,1235,1355,1481,1613,1751,1895,2040,1923,1778,1518,1257,1380,1394,1401,1408,1415,1422,1429,1436,1443,1450,1455,1460,1465,1470,1475,1480,1485,1490,1495,1499,1502,1504,1638,1777,1921,2061,2154,2200,2228,2235,2217,2182,2116,1987,1839,1696,1559,1428,1303,1184,1071,964,863,768,678,594,516,444,378,318,263,183,102,135,149,155,160,164,167,169,213,262,316,376,442,514,592,676,765,860,961,1068,1181,1300,1425,1556,1693,1836,1984,2113,1990,1842,1699,1562,1431,1306,1187,1074,967,866,767,671,581,497,419,347,273,175,218,258,253,248,241,234,219,174,217,268,324,385,451,523,601,685,775,871,973,1080,1193,1312,1437,1568,1705,1848,1996,2123,2189,2223,2238,2232,2207,2166,2087,1951,1788,1510,1643,1773,1768,1763,1758,1753,1748,1743,1738,1733,1728,1722,1715,1708,1701,1694,1687,1680,1673,1666,1659,1644,1509,1642,1783,1929,2033,1888,1744,1606,1474,1348,1228,1114,1006,903,727,550,631,645,652,659,666,673,679,684,689,694,699,704,708,711,713,805,902,1004,1112,1226,1346,1472,1604,1742,1886,1941,1792,1649,1512,1381,1256,1137,1024,917,816,721,632,549,472,401,336,277,224,177,136,101,72,49,30,17,9,3)
Polycyclic presentation:
2,3,2239|c^a=c^2238,c^b=c^295
Conjugacy classes & character table
379 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13434, 1);
Finite Group Databasebeta