← Prev (#34064345) Next (#34064347) →
D9644 #34064346
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2415 points:
(1,2,3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415);(2,4)(6,2415)(7,2414)(8,2413)(9,2412)(10,2411)(11,2410)(12,2409)(13,2408)(14,2407)(15,2406)(16,2405)(17,2404)(18,2403)(19,2402)(20,2401)(21,2400)(22,2399)(23,2398)(24,2397)(25,2396)(26,2395)(27,2394)(28,2393)(29,2392)(30,2391)(31,2390)(32,2389)(33,2388)(34,2387)(35,2386)(36,2385)(37,2384)(38,2383)(39,2382)(40,2381)(41,2380)(42,2379)(43,2378)(44,2377)(45,2376)(46,2375)(47,2374)(48,2373)(49,2372)(50,2371)(51,2370)(52,2369)(53,2368)(54,2367)(55,2366)(56,2365)(57,2364)(58,2363)(59,2362)(60,2361)(61,2360)(62,2359)(63,2358)(64,2357)(65,2356)(66,2355)(67,2354)(68,2353)(69,2352)(70,2351)(71,2350)(72,2349)(73,2348)(74,2347)(75,2346)(76,2345)(77,2344)(78,2343)(79,2342)(80,2341)(81,2340)(82,2339)(83,2338)(84,2337)(85,2336)(86,2335)(87,2334)(88,2333)(89,2332)(90,2331)(91,2330)(92,2329)(93,2328)(94,2327)(95,2326)(96,2325)(97,2324)(98,2323)(99,2322)(100,2321)(101,2320)(102,2319)(103,2318)(104,2317)(105,2316)(106,2315)(107,2314)(108,2313)(109,2312)(110,2311)(111,2310)(112,2309)(113,2308)(114,2307)(115,2306)(116,2305)(117,2304)(118,2303)(119,2302)(120,2301)(121,2300)(122,2299)(123,2298)(124,2297)(125,2296)(126,2295)(127,2294)(128,2293)(129,2292)(130,2291)(131,2290)(132,2289)(133,2288)(134,2287)(135,2286)(136,2285)(137,2284)(138,2283)(139,2282)(140,2281)(141,2280)(142,2279)(143,2278)(144,2277)(145,2276)(146,2275)(147,2274)(148,2273)(149,2272)(150,2271)(151,2270)(152,2269)(153,2268)(154,2267)(155,2266)(156,2265)(157,2264)(158,2263)(159,2262)(160,2261)(161,2260)(162,2259)(163,2258)(164,2257)(165,2256)(166,2255)(167,2254)(168,2253)(169,2252)(170,2251)(171,2250)(172,2249)(173,2248)(174,2247)(175,2246)(176,2245)(177,2244)(178,2243)(179,2242)(180,2241)(181,2240)(182,2239)(183,2238)(184,2237)(185,2236)(186,2235)(187,2234)(188,2233)(189,2232)(190,2231)(191,2230)(192,2229)(193,2228)(194,2227)(195,2226)(196,2225)(197,2224)(198,2223)(199,2222)(200,2221)(201,2220)(202,2219)(203,2218)(204,2217)(205,2216)(206,2215)(207,2214)(208,2213)(209,2212)(210,2211)(211,2210)(212,2209)(213,2208)(214,2207)(215,2206)(216,2205)(217,2204)(218,2203)(219,2202)(220,2201)(221,2200)(222,2199)(223,2198)(224,2197)(225,2196)(226,2195)(227,2194)(228,2193)(229,2192)(230,2191)(231,2190)(232,2189)(233,2188)(234,2187)(235,2186)(236,2185)(237,2184)(238,2183)(239,2182)(240,2181)(241,2180)(242,2179)(243,2178)(244,2177)(245,2176)(246,2175)(247,2174)(248,2173)(249,2172)(250,2171)(251,2170)(252,2169)(253,2168)(254,2167)(255,2166)(256,2165)(257,2164)(258,2163)(259,2162)(260,2161)(261,2160)(262,2159)(263,2158)(264,2157)(265,2156)(266,2155)(267,2154)(268,2153)(269,2152)(270,2151)(271,2150)(272,2149)(273,2148)(274,2147)(275,2146)(276,2145)(277,2144)(278,2143)(279,2142)(280,2141)(281,2140)(282,2139)(283,2138)(284,2137)(285,2136)(286,2135)(287,2134)(288,2133)(289,2132)(290,2131)(291,2130)(292,2129)(293,2128)(294,2127)(295,2126)(296,2125)(297,2124)(298,2123)(299,2122)(300,2121)(301,2120)(302,2119)(303,2118)(304,2117)(305,2116)(306,2115)(307,2114)(308,2113)(309,2112)(310,2111)(311,2110)(312,2109)(313,2108)(314,2107)(315,2106)(316,2105)(317,2104)(318,2103)(319,2102)(320,2101)(321,2100)(322,2099)(323,2098)(324,2097)(325,2096)(326,2095)(327,2094)(328,2093)(329,2092)(330,2091)(331,2090)(332,2089)(333,2088)(334,2087)(335,2086)(336,2085)(337,2084)(338,2083)(339,2082)(340,2081)(341,2080)(342,2079)(343,2078)(344,2077)(345,2076)(346,2075)(347,2074)(348,2073)(349,2072)(350,2071)(351,2070)(352,2069)(353,2068)(354,2067)(355,2066)(356,2065)(357,2064)(358,2063)(359,2062)(360,2061)(361,2060)(362,2059)(363,2058)(364,2057)(365,2056)(366,2055)(367,2054)(368,2053)(369,2052)(370,2051)(371,2050)(372,2049)(373,2048)(374,2047)(375,2046)(376,2045)(377,2044)(378,2043)(379,2042)(380,2041)(381,2040)(382,2039)(383,2038)(384,2037)(385,2036)(386,2035)(387,2034)(388,2033)(389,2032)(390,2031)(391,2030)(392,2029)(393,2028)(394,2027)(395,2026)(396,2025)(397,2024)(398,2023)(399,2022)(400,2021)(401,2020)(402,2019)(403,2018)(404,2017)(405,2016)(406,2015)(407,2014)(408,2013)(409,2012)(410,2011)(411,2010)(412,2009)(413,2008)(414,2007)(415,2006)(416,2005)(417,2004)(418,2003)(419,2002)(420,2001)(421,2000)(422,1999)(423,1998)(424,1997)(425,1996)(426,1995)(427,1994)(428,1993)(429,1992)(430,1991)(431,1990)(432,1989)(433,1988)(434,1987)(435,1986)(436,1985)(437,1984)(438,1983)(439,1982)(440,1981)(441,1980)(442,1979)(443,1978)(444,1977)(445,1976)(446,1975)(447,1974)(448,1973)(449,1972)(450,1971)(451,1970)(452,1969)(453,1968)(454,1967)(455,1966)(456,1965)(457,1964)(458,1963)(459,1962)(460,1961)(461,1960)(462,1959)(463,1958)(464,1957)(465,1956)(466,1955)(467,1954)(468,1953)(469,1952)(470,1951)(471,1950)(472,1949)(473,1948)(474,1947)(475,1946)(476,1945)(477,1944)(478,1943)(479,1942)(480,1941)(481,1940)(482,1939)(483,1938)(484,1937)(485,1936)(486,1935)(487,1934)(488,1933)(489,1932)(490,1931)(491,1930)(492,1929)(493,1928)(494,1927)(495,1926)(496,1925)(497,1924)(498,1923)(499,1922)(500,1921)(501,1920)(502,1919)(503,1918)(504,1917)(505,1916)(506,1915)(507,1914)(508,1913)(509,1912)(510,1911)(511,1910)(512,1909)(513,1908)(514,1907)(515,1906)(516,1905)(517,1904)(518,1903)(519,1902)(520,1901)(521,1900)(522,1899)(523,1898)(524,1897)(525,1896)(526,1895)(527,1894)(528,1893)(529,1892)(530,1891)(531,1890)(532,1889)(533,1888)(534,1887)(535,1886)(536,1885)(537,1884)(538,1883)(539,1882)(540,1881)(541,1880)(542,1879)(543,1878)(544,1877)(545,1876)(546,1875)(547,1874)(548,1873)(549,1872)(550,1871)(551,1870)(552,1869)(553,1868)(554,1867)(555,1866)(556,1865)(557,1864)(558,1863)(559,1862)(560,1861)(561,1860)(562,1859)(563,1858)(564,1857)(565,1856)(566,1855)(567,1854)(568,1853)(569,1852)(570,1851)(571,1850)(572,1849)(573,1848)(574,1847)(575,1846)(576,1845)(577,1844)(578,1843)(579,1842)(580,1841)(581,1840)(582,1839)(583,1838)(584,1837)(585,1836)(586,1835)(587,1834)(588,1833)(589,1832)(590,1831)(591,1830)(592,1829)(593,1828)(594,1827)(595,1826)(596,1825)(597,1824)(598,1823)(599,1822)(600,1821)(601,1820)(602,1819)(603,1818)(604,1817)(605,1816)(606,1815)(607,1814)(608,1813)(609,1812)(610,1811)(611,1810)(612,1809)(613,1808)(614,1807)(615,1806)(616,1805)(617,1804)(618,1803)(619,1802)(620,1801)(621,1800)(622,1799)(623,1798)(624,1797)(625,1796)(626,1795)(627,1794)(628,1793)(629,1792)(630,1791)(631,1790)(632,1789)(633,1788)(634,1787)(635,1786)(636,1785)(637,1784)(638,1783)(639,1782)(640,1781)(641,1780)(642,1779)(643,1778)(644,1777)(645,1776)(646,1775)(647,1774)(648,1773)(649,1772)(650,1771)(651,1770)(652,1769)(653,1768)(654,1767)(655,1766)(656,1765)(657,1764)(658,1763)(659,1762)(660,1761)(661,1760)(662,1759)(663,1758)(664,1757)(665,1756)(666,1755)(667,1754)(668,1753)(669,1752)(670,1751)(671,1750)(672,1749)(673,1748)(674,1747)(675,1746)(676,1745)(677,1744)(678,1743)(679,1742)(680,1741)(681,1740)(682,1739)(683,1738)(684,1737)(685,1736)(686,1735)(687,1734)(688,1733)(689,1732)(690,1731)(691,1730)(692,1729)(693,1728)(694,1727)(695,1726)(696,1725)(697,1724)(698,1723)(699,1722)(700,1721)(701,1720)(702,1719)(703,1718)(704,1717)(705,1716)(706,1715)(707,1714)(708,1713)(709,1712)(710,1711)(711,1710)(712,1709)(713,1708)(714,1707)(715,1706)(716,1705)(717,1704)(718,1703)(719,1702)(720,1701)(721,1700)(722,1699)(723,1698)(724,1697)(725,1696)(726,1695)(727,1694)(728,1693)(729,1692)(730,1691)(731,1690)(732,1689)(733,1688)(734,1687)(735,1686)(736,1685)(737,1684)(738,1683)(739,1682)(740,1681)(741,1680)(742,1679)(743,1678)(744,1677)(745,1676)(746,1675)(747,1674)(748,1673)(749,1672)(750,1671)(751,1670)(752,1669)(753,1668)(754,1667)(755,1666)(756,1665)(757,1664)(758,1663)(759,1662)(760,1661)(761,1660)(762,1659)(763,1658)(764,1657)(765,1656)(766,1655)(767,1654)(768,1653)(769,1652)(770,1651)(771,1650)(772,1649)(773,1648)(774,1647)(775,1646)(776,1645)(777,1644)(778,1643)(779,1642)(780,1641)(781,1640)(782,1639)(783,1638)(784,1637)(785,1636)(786,1635)(787,1634)(788,1633)(789,1632)(790,1631)(791,1630)(792,1629)(793,1628)(794,1627)(795,1626)(796,1625)(797,1624)(798,1623)(799,1622)(800,1621)(801,1620)(802,1619)(803,1618)(804,1617)(805,1616)(806,1615)(807,1614)(808,1613)(809,1612)(810,1611)(811,1610)(812,1609)(813,1608)(814,1607)(815,1606)(816,1605)(817,1604)(818,1603)(819,1602)(820,1601)(821,1600)(822,1599)(823,1598)(824,1597)(825,1596)(826,1595)(827,1594)(828,1593)(829,1592)(830,1591)(831,1590)(832,1589)(833,1588)(834,1587)(835,1586)(836,1585)(837,1584)(838,1583)(839,1582)(840,1581)(841,1580)(842,1579)(843,1578)(844,1577)(845,1576)(846,1575)(847,1574)(848,1573)(849,1572)(850,1571)(851,1570)(852,1569)(853,1568)(854,1567)(855,1566)(856,1565)(857,1564)(858,1563)(859,1562)(860,1561)(861,1560)(862,1559)(863,1558)(864,1557)(865,1556)(866,1555)(867,1554)(868,1553)(869,1552)(870,1551)(871,1550)(872,1549)(873,1548)(874,1547)(875,1546)(876,1545)(877,1544)(878,1543)(879,1542)(880,1541)(881,1540)(882,1539)(883,1538)(884,1537)(885,1536)(886,1535)(887,1534)(888,1533)(889,1532)(890,1531)(891,1530)(892,1529)(893,1528)(894,1527)(895,1526)(896,1525)(897,1524)(898,1523)(899,1522)(900,1521)(901,1520)(902,1519)(903,1518)(904,1517)(905,1516)(906,1515)(907,1514)(908,1513)(909,1512)(910,1511)(911,1510)(912,1509)(913,1508)(914,1507)(915,1506)(916,1505)(917,1504)(918,1503)(919,1502)(920,1501)(921,1500)(922,1499)(923,1498)(924,1497)(925,1496)(926,1495)(927,1494)(928,1493)(929,1492)(930,1491)(931,1490)(932,1489)(933,1488)(934,1487)(935,1486)(936,1485)(937,1484)(938,1483)(939,1482)(940,1481)(941,1480)(942,1479)(943,1478)(944,1477)(945,1476)(946,1475)(947,1474)(948,1473)(949,1472)(950,1471)(951,1470)(952,1469)(953,1468)(954,1467)(955,1466)(956,1465)(957,1464)(958,1463)(959,1462)(960,1461)(961,1460)(962,1459)(963,1458)(964,1457)(965,1456)(966,1455)(967,1454)(968,1453)(969,1452)(970,1451)(971,1450)(972,1449)(973,1448)(974,1447)(975,1446)(976,1445)(977,1444)(978,1443)(979,1442)(980,1441)(981,1440)(982,1439)(983,1438)(984,1437)(985,1436)(986,1435)(987,1434)(988,1433)(989,1432)(990,1431)(991,1430)(992,1429)(993,1428)(994,1427)(995,1426)(996,1425)(997,1424)(998,1423)(999,1422)(1000,1421)(1001,1420)(1002,1419)(1003,1418)(1004,1417)(1005,1416)(1006,1415)(1007,1414)(1008,1413)(1009,1412)(1010,1411)(1011,1410)(1012,1409)(1013,1408)(1014,1407)(1015,1406)(1016,1405)(1017,1404)(1018,1403)(1019,1402)(1020,1401)(1021,1400)(1022,1399)(1023,1398)(1024,1397)(1025,1396)(1026,1395)(1027,1394)(1028,1393)(1029,1392)(1030,1391)(1031,1390)(1032,1389)(1033,1388)(1034,1387)(1035,1386)(1036,1385)(1037,1384)(1038,1383)(1039,1382)(1040,1381)(1041,1380)(1042,1379)(1043,1378)(1044,1377)(1045,1376)(1046,1375)(1047,1374)(1048,1373)(1049,1372)(1050,1371)(1051,1370)(1052,1369)(1053,1368)(1054,1367)(1055,1366)(1056,1365)(1057,1364)(1058,1363)(1059,1362)(1060,1361)(1061,1360)(1062,1359)(1063,1358)(1064,1357)(1065,1356)(1066,1355)(1067,1354)(1068,1353)(1069,1352)(1070,1351)(1071,1350)(1072,1349)(1073,1348)(1074,1347)(1075,1346)(1076,1345)(1077,1344)(1078,1343)(1079,1342)(1080,1341)(1081,1340)(1082,1339)(1083,1338)(1084,1337)(1085,1336)(1086,1335)(1087,1334)(1088,1333)(1089,1332)(1090,1331)(1091,1330)(1092,1329)(1093,1328)(1094,1327)(1095,1326)(1096,1325)(1097,1324)(1098,1323)(1099,1322)(1100,1321)(1101,1320)(1102,1319)(1103,1318)(1104,1317)(1105,1316)(1106,1315)(1107,1314)(1108,1313)(1109,1312)(1110,1311)(1111,1310)(1112,1309)(1113,1308)(1114,1307)(1115,1306)(1116,1305)(1117,1304)(1118,1303)(1119,1302)(1120,1301)(1121,1300)(1122,1299)(1123,1298)(1124,1297)(1125,1296)(1126,1295)(1127,1294)(1128,1293)(1129,1292)(1130,1291)(1131,1290)(1132,1289)(1133,1288)(1134,1287)(1135,1286)(1136,1285)(1137,1284)(1138,1283)(1139,1282)(1140,1281)(1141,1280)(1142,1279)(1143,1278)(1144,1277)(1145,1276)(1146,1275)(1147,1274)(1148,1273)(1149,1272)(1150,1271)(1151,1270)(1152,1269)(1153,1268)(1154,1267)(1155,1266)(1156,1265)(1157,1264)(1158,1263)(1159,1262)(1160,1261)(1161,1260)(1162,1259)(1163,1258)(1164,1257)(1165,1256)(1166,1255)(1167,1254)(1168,1253)(1169,1252)(1170,1251)(1171,1250)(1172,1249)(1173,1248)(1174,1247)(1175,1246)(1176,1245)(1177,1244)(1178,1243)(1179,1242)(1180,1241)(1181,1240)(1182,1239)(1183,1238)(1184,1237)(1185,1236)(1186,1235)(1187,1234)(1188,1233)(1189,1232)(1190,1231)(1191,1230)(1192,1229)(1193,1228)(1194,1227)(1195,1226)(1196,1225)(1197,1224)(1198,1223)(1199,1222)(1200,1221)(1201,1220)(1202,1219)(1203,1218)(1204,1217)(1205,1216)(1206,1215)(1207,1214)(1208,1213)(1209,1212)(1210,1211)
Polycyclic presentation:
2^3,2411|b^a=bc,d^a=d^2410,d^b=d^2410
Conjugacy classes & character table
4825 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19288, 10);
Finite Group Databasebeta