← Prev (#44569240) Next (#44569242) →
Dic8097 #44569241
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2706 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706);(1,3,2,4)(6,7)(9,2706)(10,2705)(11,2704)(12,2703)(13,2702)(14,2701)(15,2700)(16,2699)(17,2698)(18,2697)(19,2696)(20,2695)(21,2694)(22,2693)(23,2692)(24,2691)(25,2690)(26,2689)(27,2688)(28,2687)(29,2686)(30,2685)(31,2684)(32,2683)(33,2682)(34,2681)(35,2680)(36,2679)(37,2678)(38,2677)(39,2676)(40,2675)(41,2674)(42,2673)(43,2672)(44,2671)(45,2670)(46,2669)(47,2668)(48,2667)(49,2666)(50,2665)(51,2664)(52,2663)(53,2662)(54,2661)(55,2660)(56,2659)(57,2658)(58,2657)(59,2656)(60,2655)(61,2654)(62,2653)(63,2652)(64,2651)(65,2650)(66,2649)(67,2648)(68,2647)(69,2646)(70,2645)(71,2644)(72,2643)(73,2642)(74,2641)(75,2640)(76,2639)(77,2638)(78,2637)(79,2636)(80,2635)(81,2634)(82,2633)(83,2632)(84,2631)(85,2630)(86,2629)(87,2628)(88,2627)(89,2626)(90,2625)(91,2624)(92,2623)(93,2622)(94,2621)(95,2620)(96,2619)(97,2618)(98,2617)(99,2616)(100,2615)(101,2614)(102,2613)(103,2612)(104,2611)(105,2610)(106,2609)(107,2608)(108,2607)(109,2606)(110,2605)(111,2604)(112,2603)(113,2602)(114,2601)(115,2600)(116,2599)(117,2598)(118,2597)(119,2596)(120,2595)(121,2594)(122,2593)(123,2592)(124,2591)(125,2590)(126,2589)(127,2588)(128,2587)(129,2586)(130,2585)(131,2584)(132,2583)(133,2582)(134,2581)(135,2580)(136,2579)(137,2578)(138,2577)(139,2576)(140,2575)(141,2574)(142,2573)(143,2572)(144,2571)(145,2570)(146,2569)(147,2568)(148,2567)(149,2566)(150,2565)(151,2564)(152,2563)(153,2562)(154,2561)(155,2560)(156,2559)(157,2558)(158,2557)(159,2556)(160,2555)(161,2554)(162,2553)(163,2552)(164,2551)(165,2550)(166,2549)(167,2548)(168,2547)(169,2546)(170,2545)(171,2544)(172,2543)(173,2542)(174,2541)(175,2540)(176,2539)(177,2538)(178,2537)(179,2536)(180,2535)(181,2534)(182,2533)(183,2532)(184,2531)(185,2530)(186,2529)(187,2528)(188,2527)(189,2526)(190,2525)(191,2524)(192,2523)(193,2522)(194,2521)(195,2520)(196,2519)(197,2518)(198,2517)(199,2516)(200,2515)(201,2514)(202,2513)(203,2512)(204,2511)(205,2510)(206,2509)(207,2508)(208,2507)(209,2506)(210,2505)(211,2504)(212,2503)(213,2502)(214,2501)(215,2500)(216,2499)(217,2498)(218,2497)(219,2496)(220,2495)(221,2494)(222,2493)(223,2492)(224,2491)(225,2490)(226,2489)(227,2488)(228,2487)(229,2486)(230,2485)(231,2484)(232,2483)(233,2482)(234,2481)(235,2480)(236,2479)(237,2478)(238,2477)(239,2476)(240,2475)(241,2474)(242,2473)(243,2472)(244,2471)(245,2470)(246,2469)(247,2468)(248,2467)(249,2466)(250,2465)(251,2464)(252,2463)(253,2462)(254,2461)(255,2460)(256,2459)(257,2458)(258,2457)(259,2456)(260,2455)(261,2454)(262,2453)(263,2452)(264,2451)(265,2450)(266,2449)(267,2448)(268,2447)(269,2446)(270,2445)(271,2444)(272,2443)(273,2442)(274,2441)(275,2440)(276,2439)(277,2438)(278,2437)(279,2436)(280,2435)(281,2434)(282,2433)(283,2432)(284,2431)(285,2430)(286,2429)(287,2428)(288,2427)(289,2426)(290,2425)(291,2424)(292,2423)(293,2422)(294,2421)(295,2420)(296,2419)(297,2418)(298,2417)(299,2416)(300,2415)(301,2414)(302,2413)(303,2412)(304,2411)(305,2410)(306,2409)(307,2408)(308,2407)(309,2406)(310,2405)(311,2404)(312,2403)(313,2402)(314,2401)(315,2400)(316,2399)(317,2398)(318,2397)(319,2396)(320,2395)(321,2394)(322,2393)(323,2392)(324,2391)(325,2390)(326,2389)(327,2388)(328,2387)(329,2386)(330,2385)(331,2384)(332,2383)(333,2382)(334,2381)(335,2380)(336,2379)(337,2378)(338,2377)(339,2376)(340,2375)(341,2374)(342,2373)(343,2372)(344,2371)(345,2370)(346,2369)(347,2368)(348,2367)(349,2366)(350,2365)(351,2364)(352,2363)(353,2362)(354,2361)(355,2360)(356,2359)(357,2358)(358,2357)(359,2356)(360,2355)(361,2354)(362,2353)(363,2352)(364,2351)(365,2350)(366,2349)(367,2348)(368,2347)(369,2346)(370,2345)(371,2344)(372,2343)(373,2342)(374,2341)(375,2340)(376,2339)(377,2338)(378,2337)(379,2336)(380,2335)(381,2334)(382,2333)(383,2332)(384,2331)(385,2330)(386,2329)(387,2328)(388,2327)(389,2326)(390,2325)(391,2324)(392,2323)(393,2322)(394,2321)(395,2320)(396,2319)(397,2318)(398,2317)(399,2316)(400,2315)(401,2314)(402,2313)(403,2312)(404,2311)(405,2310)(406,2309)(407,2308)(408,2307)(409,2306)(410,2305)(411,2304)(412,2303)(413,2302)(414,2301)(415,2300)(416,2299)(417,2298)(418,2297)(419,2296)(420,2295)(421,2294)(422,2293)(423,2292)(424,2291)(425,2290)(426,2289)(427,2288)(428,2287)(429,2286)(430,2285)(431,2284)(432,2283)(433,2282)(434,2281)(435,2280)(436,2279)(437,2278)(438,2277)(439,2276)(440,2275)(441,2274)(442,2273)(443,2272)(444,2271)(445,2270)(446,2269)(447,2268)(448,2267)(449,2266)(450,2265)(451,2264)(452,2263)(453,2262)(454,2261)(455,2260)(456,2259)(457,2258)(458,2257)(459,2256)(460,2255)(461,2254)(462,2253)(463,2252)(464,2251)(465,2250)(466,2249)(467,2248)(468,2247)(469,2246)(470,2245)(471,2244)(472,2243)(473,2242)(474,2241)(475,2240)(476,2239)(477,2238)(478,2237)(479,2236)(480,2235)(481,2234)(482,2233)(483,2232)(484,2231)(485,2230)(486,2229)(487,2228)(488,2227)(489,2226)(490,2225)(491,2224)(492,2223)(493,2222)(494,2221)(495,2220)(496,2219)(497,2218)(498,2217)(499,2216)(500,2215)(501,2214)(502,2213)(503,2212)(504,2211)(505,2210)(506,2209)(507,2208)(508,2207)(509,2206)(510,2205)(511,2204)(512,2203)(513,2202)(514,2201)(515,2200)(516,2199)(517,2198)(518,2197)(519,2196)(520,2195)(521,2194)(522,2193)(523,2192)(524,2191)(525,2190)(526,2189)(527,2188)(528,2187)(529,2186)(530,2185)(531,2184)(532,2183)(533,2182)(534,2181)(535,2180)(536,2179)(537,2178)(538,2177)(539,2176)(540,2175)(541,2174)(542,2173)(543,2172)(544,2171)(545,2170)(546,2169)(547,2168)(548,2167)(549,2166)(550,2165)(551,2164)(552,2163)(553,2162)(554,2161)(555,2160)(556,2159)(557,2158)(558,2157)(559,2156)(560,2155)(561,2154)(562,2153)(563,2152)(564,2151)(565,2150)(566,2149)(567,2148)(568,2147)(569,2146)(570,2145)(571,2144)(572,2143)(573,2142)(574,2141)(575,2140)(576,2139)(577,2138)(578,2137)(579,2136)(580,2135)(581,2134)(582,2133)(583,2132)(584,2131)(585,2130)(586,2129)(587,2128)(588,2127)(589,2126)(590,2125)(591,2124)(592,2123)(593,2122)(594,2121)(595,2120)(596,2119)(597,2118)(598,2117)(599,2116)(600,2115)(601,2114)(602,2113)(603,2112)(604,2111)(605,2110)(606,2109)(607,2108)(608,2107)(609,2106)(610,2105)(611,2104)(612,2103)(613,2102)(614,2101)(615,2100)(616,2099)(617,2098)(618,2097)(619,2096)(620,2095)(621,2094)(622,2093)(623,2092)(624,2091)(625,2090)(626,2089)(627,2088)(628,2087)(629,2086)(630,2085)(631,2084)(632,2083)(633,2082)(634,2081)(635,2080)(636,2079)(637,2078)(638,2077)(639,2076)(640,2075)(641,2074)(642,2073)(643,2072)(644,2071)(645,2070)(646,2069)(647,2068)(648,2067)(649,2066)(650,2065)(651,2064)(652,2063)(653,2062)(654,2061)(655,2060)(656,2059)(657,2058)(658,2057)(659,2056)(660,2055)(661,2054)(662,2053)(663,2052)(664,2051)(665,2050)(666,2049)(667,2048)(668,2047)(669,2046)(670,2045)(671,2044)(672,2043)(673,2042)(674,2041)(675,2040)(676,2039)(677,2038)(678,2037)(679,2036)(680,2035)(681,2034)(682,2033)(683,2032)(684,2031)(685,2030)(686,2029)(687,2028)(688,2027)(689,2026)(690,2025)(691,2024)(692,2023)(693,2022)(694,2021)(695,2020)(696,2019)(697,2018)(698,2017)(699,2016)(700,2015)(701,2014)(702,2013)(703,2012)(704,2011)(705,2010)(706,2009)(707,2008)(708,2007)(709,2006)(710,2005)(711,2004)(712,2003)(713,2002)(714,2001)(715,2000)(716,1999)(717,1998)(718,1997)(719,1996)(720,1995)(721,1994)(722,1993)(723,1992)(724,1991)(725,1990)(726,1989)(727,1988)(728,1987)(729,1986)(730,1985)(731,1984)(732,1983)(733,1982)(734,1981)(735,1980)(736,1979)(737,1978)(738,1977)(739,1976)(740,1975)(741,1974)(742,1973)(743,1972)(744,1971)(745,1970)(746,1969)(747,1968)(748,1967)(749,1966)(750,1965)(751,1964)(752,1963)(753,1962)(754,1961)(755,1960)(756,1959)(757,1958)(758,1957)(759,1956)(760,1955)(761,1954)(762,1953)(763,1952)(764,1951)(765,1950)(766,1949)(767,1948)(768,1947)(769,1946)(770,1945)(771,1944)(772,1943)(773,1942)(774,1941)(775,1940)(776,1939)(777,1938)(778,1937)(779,1936)(780,1935)(781,1934)(782,1933)(783,1932)(784,1931)(785,1930)(786,1929)(787,1928)(788,1927)(789,1926)(790,1925)(791,1924)(792,1923)(793,1922)(794,1921)(795,1920)(796,1919)(797,1918)(798,1917)(799,1916)(800,1915)(801,1914)(802,1913)(803,1912)(804,1911)(805,1910)(806,1909)(807,1908)(808,1907)(809,1906)(810,1905)(811,1904)(812,1903)(813,1902)(814,1901)(815,1900)(816,1899)(817,1898)(818,1897)(819,1896)(820,1895)(821,1894)(822,1893)(823,1892)(824,1891)(825,1890)(826,1889)(827,1888)(828,1887)(829,1886)(830,1885)(831,1884)(832,1883)(833,1882)(834,1881)(835,1880)(836,1879)(837,1878)(838,1877)(839,1876)(840,1875)(841,1874)(842,1873)(843,1872)(844,1871)(845,1870)(846,1869)(847,1868)(848,1867)(849,1866)(850,1865)(851,1864)(852,1863)(853,1862)(854,1861)(855,1860)(856,1859)(857,1858)(858,1857)(859,1856)(860,1855)(861,1854)(862,1853)(863,1852)(864,1851)(865,1850)(866,1849)(867,1848)(868,1847)(869,1846)(870,1845)(871,1844)(872,1843)(873,1842)(874,1841)(875,1840)(876,1839)(877,1838)(878,1837)(879,1836)(880,1835)(881,1834)(882,1833)(883,1832)(884,1831)(885,1830)(886,1829)(887,1828)(888,1827)(889,1826)(890,1825)(891,1824)(892,1823)(893,1822)(894,1821)(895,1820)(896,1819)(897,1818)(898,1817)(899,1816)(900,1815)(901,1814)(902,1813)(903,1812)(904,1811)(905,1810)(906,1809)(907,1808)(908,1807)(909,1806)(910,1805)(911,1804)(912,1803)(913,1802)(914,1801)(915,1800)(916,1799)(917,1798)(918,1797)(919,1796)(920,1795)(921,1794)(922,1793)(923,1792)(924,1791)(925,1790)(926,1789)(927,1788)(928,1787)(929,1786)(930,1785)(931,1784)(932,1783)(933,1782)(934,1781)(935,1780)(936,1779)(937,1778)(938,1777)(939,1776)(940,1775)(941,1774)(942,1773)(943,1772)(944,1771)(945,1770)(946,1769)(947,1768)(948,1767)(949,1766)(950,1765)(951,1764)(952,1763)(953,1762)(954,1761)(955,1760)(956,1759)(957,1758)(958,1757)(959,1756)(960,1755)(961,1754)(962,1753)(963,1752)(964,1751)(965,1750)(966,1749)(967,1748)(968,1747)(969,1746)(970,1745)(971,1744)(972,1743)(973,1742)(974,1741)(975,1740)(976,1739)(977,1738)(978,1737)(979,1736)(980,1735)(981,1734)(982,1733)(983,1732)(984,1731)(985,1730)(986,1729)(987,1728)(988,1727)(989,1726)(990,1725)(991,1724)(992,1723)(993,1722)(994,1721)(995,1720)(996,1719)(997,1718)(998,1717)(999,1716)(1000,1715)(1001,1714)(1002,1713)(1003,1712)(1004,1711)(1005,1710)(1006,1709)(1007,1708)(1008,1707)(1009,1706)(1010,1705)(1011,1704)(1012,1703)(1013,1702)(1014,1701)(1015,1700)(1016,1699)(1017,1698)(1018,1697)(1019,1696)(1020,1695)(1021,1694)(1022,1693)(1023,1692)(1024,1691)(1025,1690)(1026,1689)(1027,1688)(1028,1687)(1029,1686)(1030,1685)(1031,1684)(1032,1683)(1033,1682)(1034,1681)(1035,1680)(1036,1679)(1037,1678)(1038,1677)(1039,1676)(1040,1675)(1041,1674)(1042,1673)(1043,1672)(1044,1671)(1045,1670)(1046,1669)(1047,1668)(1048,1667)(1049,1666)(1050,1665)(1051,1664)(1052,1663)(1053,1662)(1054,1661)(1055,1660)(1056,1659)(1057,1658)(1058,1657)(1059,1656)(1060,1655)(1061,1654)(1062,1653)(1063,1652)(1064,1651)(1065,1650)(1066,1649)(1067,1648)(1068,1647)(1069,1646)(1070,1645)(1071,1644)(1072,1643)(1073,1642)(1074,1641)(1075,1640)(1076,1639)(1077,1638)(1078,1637)(1079,1636)(1080,1635)(1081,1634)(1082,1633)(1083,1632)(1084,1631)(1085,1630)(1086,1629)(1087,1628)(1088,1627)(1089,1626)(1090,1625)(1091,1624)(1092,1623)(1093,1622)(1094,1621)(1095,1620)(1096,1619)(1097,1618)(1098,1617)(1099,1616)(1100,1615)(1101,1614)(1102,1613)(1103,1612)(1104,1611)(1105,1610)(1106,1609)(1107,1608)(1108,1607)(1109,1606)(1110,1605)(1111,1604)(1112,1603)(1113,1602)(1114,1601)(1115,1600)(1116,1599)(1117,1598)(1118,1597)(1119,1596)(1120,1595)(1121,1594)(1122,1593)(1123,1592)(1124,1591)(1125,1590)(1126,1589)(1127,1588)(1128,1587)(1129,1586)(1130,1585)(1131,1584)(1132,1583)(1133,1582)(1134,1581)(1135,1580)(1136,1579)(1137,1578)(1138,1577)(1139,1576)(1140,1575)(1141,1574)(1142,1573)(1143,1572)(1144,1571)(1145,1570)(1146,1569)(1147,1568)(1148,1567)(1149,1566)(1150,1565)(1151,1564)(1152,1563)(1153,1562)(1154,1561)(1155,1560)(1156,1559)(1157,1558)(1158,1557)(1159,1556)(1160,1555)(1161,1554)(1162,1553)(1163,1552)(1164,1551)(1165,1550)(1166,1549)(1167,1548)(1168,1547)(1169,1546)(1170,1545)(1171,1544)(1172,1543)(1173,1542)(1174,1541)(1175,1540)(1176,1539)(1177,1538)(1178,1537)(1179,1536)(1180,1535)(1181,1534)(1182,1533)(1183,1532)(1184,1531)(1185,1530)(1186,1529)(1187,1528)(1188,1527)(1189,1526)(1190,1525)(1191,1524)(1192,1523)(1193,1522)(1194,1521)(1195,1520)(1196,1519)(1197,1518)(1198,1517)(1199,1516)(1200,1515)(1201,1514)(1202,1513)(1203,1512)(1204,1511)(1205,1510)(1206,1509)(1207,1508)(1208,1507)(1209,1506)(1210,1505)(1211,1504)(1212,1503)(1213,1502)(1214,1501)(1215,1500)(1216,1499)(1217,1498)(1218,1497)(1219,1496)(1220,1495)(1221,1494)(1222,1493)(1223,1492)(1224,1491)(1225,1490)(1226,1489)(1227,1488)(1228,1487)(1229,1486)(1230,1485)(1231,1484)(1232,1483)(1233,1482)(1234,1481)(1235,1480)(1236,1479)(1237,1478)(1238,1477)(1239,1476)(1240,1475)(1241,1474)(1242,1473)(1243,1472)(1244,1471)(1245,1470)(1246,1469)(1247,1468)(1248,1467)(1249,1466)(1250,1465)(1251,1464)(1252,1463)(1253,1462)(1254,1461)(1255,1460)(1256,1459)(1257,1458)(1258,1457)(1259,1456)(1260,1455)(1261,1454)(1262,1453)(1263,1452)(1264,1451)(1265,1450)(1266,1449)(1267,1448)(1268,1447)(1269,1446)(1270,1445)(1271,1444)(1272,1443)(1273,1442)(1274,1441)(1275,1440)(1276,1439)(1277,1438)(1278,1437)(1279,1436)(1280,1435)(1281,1434)(1282,1433)(1283,1432)(1284,1431)(1285,1430)(1286,1429)(1287,1428)(1288,1427)(1289,1426)(1290,1425)(1291,1424)(1292,1423)(1293,1422)(1294,1421)(1295,1420)(1296,1419)(1297,1418)(1298,1417)(1299,1416)(1300,1415)(1301,1414)(1302,1413)(1303,1412)(1304,1411)(1305,1410)(1306,1409)(1307,1408)(1308,1407)(1309,1406)(1310,1405)(1311,1404)(1312,1403)(1313,1402)(1314,1401)(1315,1400)(1316,1399)(1317,1398)(1318,1397)(1319,1396)(1320,1395)(1321,1394)(1322,1393)(1323,1392)(1324,1391)(1325,1390)(1326,1389)(1327,1388)(1328,1387)(1329,1386)(1330,1385)(1331,1384)(1332,1383)(1333,1382)(1334,1381)(1335,1380)(1336,1379)(1337,1378)(1338,1377)(1339,1376)(1340,1375)(1341,1374)(1342,1373)(1343,1372)(1344,1371)(1345,1370)(1346,1369)(1347,1368)(1348,1367)(1349,1366)(1350,1365)(1351,1364)(1352,1363)(1353,1362)(1354,1361)(1355,1360)(1356,1359)(1357,1358)
Polycyclic presentation:
2,3,2699,2|a^2=d,b^a=b^2,c^a=c^2698
Conjugacy classes & character table
8100 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32388, 4);
Finite Group Databasebeta