← Prev (#44540900) Next (#44540902) →
Dic7941 #44540901
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2654 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654);(1,3,2,4)(6,7)(9,2654)(10,2653)(11,2652)(12,2651)(13,2650)(14,2649)(15,2648)(16,2647)(17,2646)(18,2645)(19,2644)(20,2643)(21,2642)(22,2641)(23,2640)(24,2639)(25,2638)(26,2637)(27,2636)(28,2635)(29,2634)(30,2633)(31,2632)(32,2631)(33,2630)(34,2629)(35,2628)(36,2627)(37,2626)(38,2625)(39,2624)(40,2623)(41,2622)(42,2621)(43,2620)(44,2619)(45,2618)(46,2617)(47,2616)(48,2615)(49,2614)(50,2613)(51,2612)(52,2611)(53,2610)(54,2609)(55,2608)(56,2607)(57,2606)(58,2605)(59,2604)(60,2603)(61,2602)(62,2601)(63,2600)(64,2599)(65,2598)(66,2597)(67,2596)(68,2595)(69,2594)(70,2593)(71,2592)(72,2591)(73,2590)(74,2589)(75,2588)(76,2587)(77,2586)(78,2585)(79,2584)(80,2583)(81,2582)(82,2581)(83,2580)(84,2579)(85,2578)(86,2577)(87,2576)(88,2575)(89,2574)(90,2573)(91,2572)(92,2571)(93,2570)(94,2569)(95,2568)(96,2567)(97,2566)(98,2565)(99,2564)(100,2563)(101,2562)(102,2561)(103,2560)(104,2559)(105,2558)(106,2557)(107,2556)(108,2555)(109,2554)(110,2553)(111,2552)(112,2551)(113,2550)(114,2549)(115,2548)(116,2547)(117,2546)(118,2545)(119,2544)(120,2543)(121,2542)(122,2541)(123,2540)(124,2539)(125,2538)(126,2537)(127,2536)(128,2535)(129,2534)(130,2533)(131,2532)(132,2531)(133,2530)(134,2529)(135,2528)(136,2527)(137,2526)(138,2525)(139,2524)(140,2523)(141,2522)(142,2521)(143,2520)(144,2519)(145,2518)(146,2517)(147,2516)(148,2515)(149,2514)(150,2513)(151,2512)(152,2511)(153,2510)(154,2509)(155,2508)(156,2507)(157,2506)(158,2505)(159,2504)(160,2503)(161,2502)(162,2501)(163,2500)(164,2499)(165,2498)(166,2497)(167,2496)(168,2495)(169,2494)(170,2493)(171,2492)(172,2491)(173,2490)(174,2489)(175,2488)(176,2487)(177,2486)(178,2485)(179,2484)(180,2483)(181,2482)(182,2481)(183,2480)(184,2479)(185,2478)(186,2477)(187,2476)(188,2475)(189,2474)(190,2473)(191,2472)(192,2471)(193,2470)(194,2469)(195,2468)(196,2467)(197,2466)(198,2465)(199,2464)(200,2463)(201,2462)(202,2461)(203,2460)(204,2459)(205,2458)(206,2457)(207,2456)(208,2455)(209,2454)(210,2453)(211,2452)(212,2451)(213,2450)(214,2449)(215,2448)(216,2447)(217,2446)(218,2445)(219,2444)(220,2443)(221,2442)(222,2441)(223,2440)(224,2439)(225,2438)(226,2437)(227,2436)(228,2435)(229,2434)(230,2433)(231,2432)(232,2431)(233,2430)(234,2429)(235,2428)(236,2427)(237,2426)(238,2425)(239,2424)(240,2423)(241,2422)(242,2421)(243,2420)(244,2419)(245,2418)(246,2417)(247,2416)(248,2415)(249,2414)(250,2413)(251,2412)(252,2411)(253,2410)(254,2409)(255,2408)(256,2407)(257,2406)(258,2405)(259,2404)(260,2403)(261,2402)(262,2401)(263,2400)(264,2399)(265,2398)(266,2397)(267,2396)(268,2395)(269,2394)(270,2393)(271,2392)(272,2391)(273,2390)(274,2389)(275,2388)(276,2387)(277,2386)(278,2385)(279,2384)(280,2383)(281,2382)(282,2381)(283,2380)(284,2379)(285,2378)(286,2377)(287,2376)(288,2375)(289,2374)(290,2373)(291,2372)(292,2371)(293,2370)(294,2369)(295,2368)(296,2367)(297,2366)(298,2365)(299,2364)(300,2363)(301,2362)(302,2361)(303,2360)(304,2359)(305,2358)(306,2357)(307,2356)(308,2355)(309,2354)(310,2353)(311,2352)(312,2351)(313,2350)(314,2349)(315,2348)(316,2347)(317,2346)(318,2345)(319,2344)(320,2343)(321,2342)(322,2341)(323,2340)(324,2339)(325,2338)(326,2337)(327,2336)(328,2335)(329,2334)(330,2333)(331,2332)(332,2331)(333,2330)(334,2329)(335,2328)(336,2327)(337,2326)(338,2325)(339,2324)(340,2323)(341,2322)(342,2321)(343,2320)(344,2319)(345,2318)(346,2317)(347,2316)(348,2315)(349,2314)(350,2313)(351,2312)(352,2311)(353,2310)(354,2309)(355,2308)(356,2307)(357,2306)(358,2305)(359,2304)(360,2303)(361,2302)(362,2301)(363,2300)(364,2299)(365,2298)(366,2297)(367,2296)(368,2295)(369,2294)(370,2293)(371,2292)(372,2291)(373,2290)(374,2289)(375,2288)(376,2287)(377,2286)(378,2285)(379,2284)(380,2283)(381,2282)(382,2281)(383,2280)(384,2279)(385,2278)(386,2277)(387,2276)(388,2275)(389,2274)(390,2273)(391,2272)(392,2271)(393,2270)(394,2269)(395,2268)(396,2267)(397,2266)(398,2265)(399,2264)(400,2263)(401,2262)(402,2261)(403,2260)(404,2259)(405,2258)(406,2257)(407,2256)(408,2255)(409,2254)(410,2253)(411,2252)(412,2251)(413,2250)(414,2249)(415,2248)(416,2247)(417,2246)(418,2245)(419,2244)(420,2243)(421,2242)(422,2241)(423,2240)(424,2239)(425,2238)(426,2237)(427,2236)(428,2235)(429,2234)(430,2233)(431,2232)(432,2231)(433,2230)(434,2229)(435,2228)(436,2227)(437,2226)(438,2225)(439,2224)(440,2223)(441,2222)(442,2221)(443,2220)(444,2219)(445,2218)(446,2217)(447,2216)(448,2215)(449,2214)(450,2213)(451,2212)(452,2211)(453,2210)(454,2209)(455,2208)(456,2207)(457,2206)(458,2205)(459,2204)(460,2203)(461,2202)(462,2201)(463,2200)(464,2199)(465,2198)(466,2197)(467,2196)(468,2195)(469,2194)(470,2193)(471,2192)(472,2191)(473,2190)(474,2189)(475,2188)(476,2187)(477,2186)(478,2185)(479,2184)(480,2183)(481,2182)(482,2181)(483,2180)(484,2179)(485,2178)(486,2177)(487,2176)(488,2175)(489,2174)(490,2173)(491,2172)(492,2171)(493,2170)(494,2169)(495,2168)(496,2167)(497,2166)(498,2165)(499,2164)(500,2163)(501,2162)(502,2161)(503,2160)(504,2159)(505,2158)(506,2157)(507,2156)(508,2155)(509,2154)(510,2153)(511,2152)(512,2151)(513,2150)(514,2149)(515,2148)(516,2147)(517,2146)(518,2145)(519,2144)(520,2143)(521,2142)(522,2141)(523,2140)(524,2139)(525,2138)(526,2137)(527,2136)(528,2135)(529,2134)(530,2133)(531,2132)(532,2131)(533,2130)(534,2129)(535,2128)(536,2127)(537,2126)(538,2125)(539,2124)(540,2123)(541,2122)(542,2121)(543,2120)(544,2119)(545,2118)(546,2117)(547,2116)(548,2115)(549,2114)(550,2113)(551,2112)(552,2111)(553,2110)(554,2109)(555,2108)(556,2107)(557,2106)(558,2105)(559,2104)(560,2103)(561,2102)(562,2101)(563,2100)(564,2099)(565,2098)(566,2097)(567,2096)(568,2095)(569,2094)(570,2093)(571,2092)(572,2091)(573,2090)(574,2089)(575,2088)(576,2087)(577,2086)(578,2085)(579,2084)(580,2083)(581,2082)(582,2081)(583,2080)(584,2079)(585,2078)(586,2077)(587,2076)(588,2075)(589,2074)(590,2073)(591,2072)(592,2071)(593,2070)(594,2069)(595,2068)(596,2067)(597,2066)(598,2065)(599,2064)(600,2063)(601,2062)(602,2061)(603,2060)(604,2059)(605,2058)(606,2057)(607,2056)(608,2055)(609,2054)(610,2053)(611,2052)(612,2051)(613,2050)(614,2049)(615,2048)(616,2047)(617,2046)(618,2045)(619,2044)(620,2043)(621,2042)(622,2041)(623,2040)(624,2039)(625,2038)(626,2037)(627,2036)(628,2035)(629,2034)(630,2033)(631,2032)(632,2031)(633,2030)(634,2029)(635,2028)(636,2027)(637,2026)(638,2025)(639,2024)(640,2023)(641,2022)(642,2021)(643,2020)(644,2019)(645,2018)(646,2017)(647,2016)(648,2015)(649,2014)(650,2013)(651,2012)(652,2011)(653,2010)(654,2009)(655,2008)(656,2007)(657,2006)(658,2005)(659,2004)(660,2003)(661,2002)(662,2001)(663,2000)(664,1999)(665,1998)(666,1997)(667,1996)(668,1995)(669,1994)(670,1993)(671,1992)(672,1991)(673,1990)(674,1989)(675,1988)(676,1987)(677,1986)(678,1985)(679,1984)(680,1983)(681,1982)(682,1981)(683,1980)(684,1979)(685,1978)(686,1977)(687,1976)(688,1975)(689,1974)(690,1973)(691,1972)(692,1971)(693,1970)(694,1969)(695,1968)(696,1967)(697,1966)(698,1965)(699,1964)(700,1963)(701,1962)(702,1961)(703,1960)(704,1959)(705,1958)(706,1957)(707,1956)(708,1955)(709,1954)(710,1953)(711,1952)(712,1951)(713,1950)(714,1949)(715,1948)(716,1947)(717,1946)(718,1945)(719,1944)(720,1943)(721,1942)(722,1941)(723,1940)(724,1939)(725,1938)(726,1937)(727,1936)(728,1935)(729,1934)(730,1933)(731,1932)(732,1931)(733,1930)(734,1929)(735,1928)(736,1927)(737,1926)(738,1925)(739,1924)(740,1923)(741,1922)(742,1921)(743,1920)(744,1919)(745,1918)(746,1917)(747,1916)(748,1915)(749,1914)(750,1913)(751,1912)(752,1911)(753,1910)(754,1909)(755,1908)(756,1907)(757,1906)(758,1905)(759,1904)(760,1903)(761,1902)(762,1901)(763,1900)(764,1899)(765,1898)(766,1897)(767,1896)(768,1895)(769,1894)(770,1893)(771,1892)(772,1891)(773,1890)(774,1889)(775,1888)(776,1887)(777,1886)(778,1885)(779,1884)(780,1883)(781,1882)(782,1881)(783,1880)(784,1879)(785,1878)(786,1877)(787,1876)(788,1875)(789,1874)(790,1873)(791,1872)(792,1871)(793,1870)(794,1869)(795,1868)(796,1867)(797,1866)(798,1865)(799,1864)(800,1863)(801,1862)(802,1861)(803,1860)(804,1859)(805,1858)(806,1857)(807,1856)(808,1855)(809,1854)(810,1853)(811,1852)(812,1851)(813,1850)(814,1849)(815,1848)(816,1847)(817,1846)(818,1845)(819,1844)(820,1843)(821,1842)(822,1841)(823,1840)(824,1839)(825,1838)(826,1837)(827,1836)(828,1835)(829,1834)(830,1833)(831,1832)(832,1831)(833,1830)(834,1829)(835,1828)(836,1827)(837,1826)(838,1825)(839,1824)(840,1823)(841,1822)(842,1821)(843,1820)(844,1819)(845,1818)(846,1817)(847,1816)(848,1815)(849,1814)(850,1813)(851,1812)(852,1811)(853,1810)(854,1809)(855,1808)(856,1807)(857,1806)(858,1805)(859,1804)(860,1803)(861,1802)(862,1801)(863,1800)(864,1799)(865,1798)(866,1797)(867,1796)(868,1795)(869,1794)(870,1793)(871,1792)(872,1791)(873,1790)(874,1789)(875,1788)(876,1787)(877,1786)(878,1785)(879,1784)(880,1783)(881,1782)(882,1781)(883,1780)(884,1779)(885,1778)(886,1777)(887,1776)(888,1775)(889,1774)(890,1773)(891,1772)(892,1771)(893,1770)(894,1769)(895,1768)(896,1767)(897,1766)(898,1765)(899,1764)(900,1763)(901,1762)(902,1761)(903,1760)(904,1759)(905,1758)(906,1757)(907,1756)(908,1755)(909,1754)(910,1753)(911,1752)(912,1751)(913,1750)(914,1749)(915,1748)(916,1747)(917,1746)(918,1745)(919,1744)(920,1743)(921,1742)(922,1741)(923,1740)(924,1739)(925,1738)(926,1737)(927,1736)(928,1735)(929,1734)(930,1733)(931,1732)(932,1731)(933,1730)(934,1729)(935,1728)(936,1727)(937,1726)(938,1725)(939,1724)(940,1723)(941,1722)(942,1721)(943,1720)(944,1719)(945,1718)(946,1717)(947,1716)(948,1715)(949,1714)(950,1713)(951,1712)(952,1711)(953,1710)(954,1709)(955,1708)(956,1707)(957,1706)(958,1705)(959,1704)(960,1703)(961,1702)(962,1701)(963,1700)(964,1699)(965,1698)(966,1697)(967,1696)(968,1695)(969,1694)(970,1693)(971,1692)(972,1691)(973,1690)(974,1689)(975,1688)(976,1687)(977,1686)(978,1685)(979,1684)(980,1683)(981,1682)(982,1681)(983,1680)(984,1679)(985,1678)(986,1677)(987,1676)(988,1675)(989,1674)(990,1673)(991,1672)(992,1671)(993,1670)(994,1669)(995,1668)(996,1667)(997,1666)(998,1665)(999,1664)(1000,1663)(1001,1662)(1002,1661)(1003,1660)(1004,1659)(1005,1658)(1006,1657)(1007,1656)(1008,1655)(1009,1654)(1010,1653)(1011,1652)(1012,1651)(1013,1650)(1014,1649)(1015,1648)(1016,1647)(1017,1646)(1018,1645)(1019,1644)(1020,1643)(1021,1642)(1022,1641)(1023,1640)(1024,1639)(1025,1638)(1026,1637)(1027,1636)(1028,1635)(1029,1634)(1030,1633)(1031,1632)(1032,1631)(1033,1630)(1034,1629)(1035,1628)(1036,1627)(1037,1626)(1038,1625)(1039,1624)(1040,1623)(1041,1622)(1042,1621)(1043,1620)(1044,1619)(1045,1618)(1046,1617)(1047,1616)(1048,1615)(1049,1614)(1050,1613)(1051,1612)(1052,1611)(1053,1610)(1054,1609)(1055,1608)(1056,1607)(1057,1606)(1058,1605)(1059,1604)(1060,1603)(1061,1602)(1062,1601)(1063,1600)(1064,1599)(1065,1598)(1066,1597)(1067,1596)(1068,1595)(1069,1594)(1070,1593)(1071,1592)(1072,1591)(1073,1590)(1074,1589)(1075,1588)(1076,1587)(1077,1586)(1078,1585)(1079,1584)(1080,1583)(1081,1582)(1082,1581)(1083,1580)(1084,1579)(1085,1578)(1086,1577)(1087,1576)(1088,1575)(1089,1574)(1090,1573)(1091,1572)(1092,1571)(1093,1570)(1094,1569)(1095,1568)(1096,1567)(1097,1566)(1098,1565)(1099,1564)(1100,1563)(1101,1562)(1102,1561)(1103,1560)(1104,1559)(1105,1558)(1106,1557)(1107,1556)(1108,1555)(1109,1554)(1110,1553)(1111,1552)(1112,1551)(1113,1550)(1114,1549)(1115,1548)(1116,1547)(1117,1546)(1118,1545)(1119,1544)(1120,1543)(1121,1542)(1122,1541)(1123,1540)(1124,1539)(1125,1538)(1126,1537)(1127,1536)(1128,1535)(1129,1534)(1130,1533)(1131,1532)(1132,1531)(1133,1530)(1134,1529)(1135,1528)(1136,1527)(1137,1526)(1138,1525)(1139,1524)(1140,1523)(1141,1522)(1142,1521)(1143,1520)(1144,1519)(1145,1518)(1146,1517)(1147,1516)(1148,1515)(1149,1514)(1150,1513)(1151,1512)(1152,1511)(1153,1510)(1154,1509)(1155,1508)(1156,1507)(1157,1506)(1158,1505)(1159,1504)(1160,1503)(1161,1502)(1162,1501)(1163,1500)(1164,1499)(1165,1498)(1166,1497)(1167,1496)(1168,1495)(1169,1494)(1170,1493)(1171,1492)(1172,1491)(1173,1490)(1174,1489)(1175,1488)(1176,1487)(1177,1486)(1178,1485)(1179,1484)(1180,1483)(1181,1482)(1182,1481)(1183,1480)(1184,1479)(1185,1478)(1186,1477)(1187,1476)(1188,1475)(1189,1474)(1190,1473)(1191,1472)(1192,1471)(1193,1470)(1194,1469)(1195,1468)(1196,1467)(1197,1466)(1198,1465)(1199,1464)(1200,1463)(1201,1462)(1202,1461)(1203,1460)(1204,1459)(1205,1458)(1206,1457)(1207,1456)(1208,1455)(1209,1454)(1210,1453)(1211,1452)(1212,1451)(1213,1450)(1214,1449)(1215,1448)(1216,1447)(1217,1446)(1218,1445)(1219,1444)(1220,1443)(1221,1442)(1222,1441)(1223,1440)(1224,1439)(1225,1438)(1226,1437)(1227,1436)(1228,1435)(1229,1434)(1230,1433)(1231,1432)(1232,1431)(1233,1430)(1234,1429)(1235,1428)(1236,1427)(1237,1426)(1238,1425)(1239,1424)(1240,1423)(1241,1422)(1242,1421)(1243,1420)(1244,1419)(1245,1418)(1246,1417)(1247,1416)(1248,1415)(1249,1414)(1250,1413)(1251,1412)(1252,1411)(1253,1410)(1254,1409)(1255,1408)(1256,1407)(1257,1406)(1258,1405)(1259,1404)(1260,1403)(1261,1402)(1262,1401)(1263,1400)(1264,1399)(1265,1398)(1266,1397)(1267,1396)(1268,1395)(1269,1394)(1270,1393)(1271,1392)(1272,1391)(1273,1390)(1274,1389)(1275,1388)(1276,1387)(1277,1386)(1278,1385)(1279,1384)(1280,1383)(1281,1382)(1282,1381)(1283,1380)(1284,1379)(1285,1378)(1286,1377)(1287,1376)(1288,1375)(1289,1374)(1290,1373)(1291,1372)(1292,1371)(1293,1370)(1294,1369)(1295,1368)(1296,1367)(1297,1366)(1298,1365)(1299,1364)(1300,1363)(1301,1362)(1302,1361)(1303,1360)(1304,1359)(1305,1358)(1306,1357)(1307,1356)(1308,1355)(1309,1354)(1310,1353)(1311,1352)(1312,1351)(1313,1350)(1314,1349)(1315,1348)(1316,1347)(1317,1346)(1318,1345)(1319,1344)(1320,1343)(1321,1342)(1322,1341)(1323,1340)(1324,1339)(1325,1338)(1326,1337)(1327,1336)(1328,1335)(1329,1334)(1330,1333)(1331,1332)
Polycyclic presentation:
2,3,2647,2|a^2=d,b^a=b^2,c^a=c^2646
Conjugacy classes & character table
7944 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31764, 6);
Finite Group Databasebeta