← Prev (#44535860) Next (#44535862) →
D15685 #44535861
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3142 points:
(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,2721,2722,2723,2724,2725,2726,2727,2728,2729,2730,2731,2732,2733,2734,2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,2751,2752,2753,2754,2755,2756,2757,2758,2759,2760,2761,2762,2763,2764,2765,2766,2767,2768,2769,2770,2771,2772,2773,2774,2775,2776,2777,2778,2779,2780,2781,2782,2783,2784,2785,2786,2787,2788,2789,2790,2791,2792,2793,2794,2795,2796,2797,2798,2799,2800,2801,2802,2803,2804,2805,2806,2807,2808,2809,2810,2811,2812,2813,2814,2815,2816,2817,2818,2819,2820,2821,2822,2823,2824,2825,2826,2827,2828,2829,2830,2831,2832,2833,2834,2835,2836,2837,2838,2839,2840,2841,2842,2843,2844,2845,2846,2847,2848,2849,2850,2851,2852,2853,2854,2855,2856,2857,2858,2859,2860,2861,2862,2863,2864,2865,2866,2867,2868,2869,2870,2871,2872,2873,2874,2875,2876,2877,2878,2879,2880,2881,2882,2883,2884,2885,2886,2887,2888,2889,2890,2891,2892,2893,2894,2895,2896,2897,2898,2899,2900,2901,2902,2903,2904,2905,2906,2907,2908,2909,2910,2911,2912,2913,2914,2915,2916,2917,2918,2919,2920,2921,2922,2923,2924,2925,2926,2927,2928,2929,2930,2931,2932,2933,2934,2935,2936,2937,2938,2939,2940,2941,2942,2943,2944,2945,2946,2947,2948,2949,2950,2951,2952,2953,2954,2955,2956,2957,2958,2959,2960,2961,2962,2963,2964,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,2977,2978,2979,2980,2981,2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003,3004,3005,3006,3007,3008,3009,3010,3011,3012,3013,3014,3015,3016,3017,3018,3019,3020,3021,3022,3023,3024,3025,3026,3027,3028,3029,3030,3031,3032,3033,3034,3035,3036,3037,3038,3039,3040,3041,3042,3043,3044,3045,3046,3047,3048,3049,3050,3051,3052,3053,3054,3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,3067,3068,3069,3070,3071,3072,3073,3074,3075,3076,3077,3078,3079,3080,3081,3082,3083,3084,3085,3086,3087,3088,3089,3090,3091,3092,3093,3094,3095,3096,3097,3098,3099,3100,3101,3102,3103,3104,3105,3106,3107,3108,3109,3110,3111,3112,3113,3114,3115,3116,3117,3118,3119,3120,3121,3122,3123,3124,3125,3126,3127,3128,3129,3130,3131,3132,3133,3134,3135,3136,3137,3138,3139,3140,3141,3142);(2,5)(3,4)(7,3142)(8,3141)(9,3140)(10,3139)(11,3138)(12,3137)(13,3136)(14,3135)(15,3134)(16,3133)(17,3132)(18,3131)(19,3130)(20,3129)(21,3128)(22,3127)(23,3126)(24,3125)(25,3124)(26,3123)(27,3122)(28,3121)(29,3120)(30,3119)(31,3118)(32,3117)(33,3116)(34,3115)(35,3114)(36,3113)(37,3112)(38,3111)(39,3110)(40,3109)(41,3108)(42,3107)(43,3106)(44,3105)(45,3104)(46,3103)(47,3102)(48,3101)(49,3100)(50,3099)(51,3098)(52,3097)(53,3096)(54,3095)(55,3094)(56,3093)(57,3092)(58,3091)(59,3090)(60,3089)(61,3088)(62,3087)(63,3086)(64,3085)(65,3084)(66,3083)(67,3082)(68,3081)(69,3080)(70,3079)(71,3078)(72,3077)(73,3076)(74,3075)(75,3074)(76,3073)(77,3072)(78,3071)(79,3070)(80,3069)(81,3068)(82,3067)(83,3066)(84,3065)(85,3064)(86,3063)(87,3062)(88,3061)(89,3060)(90,3059)(91,3058)(92,3057)(93,3056)(94,3055)(95,3054)(96,3053)(97,3052)(98,3051)(99,3050)(100,3049)(101,3048)(102,3047)(103,3046)(104,3045)(105,3044)(106,3043)(107,3042)(108,3041)(109,3040)(110,3039)(111,3038)(112,3037)(113,3036)(114,3035)(115,3034)(116,3033)(117,3032)(118,3031)(119,3030)(120,3029)(121,3028)(122,3027)(123,3026)(124,3025)(125,3024)(126,3023)(127,3022)(128,3021)(129,3020)(130,3019)(131,3018)(132,3017)(133,3016)(134,3015)(135,3014)(136,3013)(137,3012)(138,3011)(139,3010)(140,3009)(141,3008)(142,3007)(143,3006)(144,3005)(145,3004)(146,3003)(147,3002)(148,3001)(149,3000)(150,2999)(151,2998)(152,2997)(153,2996)(154,2995)(155,2994)(156,2993)(157,2992)(158,2991)(159,2990)(160,2989)(161,2988)(162,2987)(163,2986)(164,2985)(165,2984)(166,2983)(167,2982)(168,2981)(169,2980)(170,2979)(171,2978)(172,2977)(173,2976)(174,2975)(175,2974)(176,2973)(177,2972)(178,2971)(179,2970)(180,2969)(181,2968)(182,2967)(183,2966)(184,2965)(185,2964)(186,2963)(187,2962)(188,2961)(189,2960)(190,2959)(191,2958)(192,2957)(193,2956)(194,2955)(195,2954)(196,2953)(197,2952)(198,2951)(199,2950)(200,2949)(201,2948)(202,2947)(203,2946)(204,2945)(205,2944)(206,2943)(207,2942)(208,2941)(209,2940)(210,2939)(211,2938)(212,2937)(213,2936)(214,2935)(215,2934)(216,2933)(217,2932)(218,2931)(219,2930)(220,2929)(221,2928)(222,2927)(223,2926)(224,2925)(225,2924)(226,2923)(227,2922)(228,2921)(229,2920)(230,2919)(231,2918)(232,2917)(233,2916)(234,2915)(235,2914)(236,2913)(237,2912)(238,2911)(239,2910)(240,2909)(241,2908)(242,2907)(243,2906)(244,2905)(245,2904)(246,2903)(247,2902)(248,2901)(249,2900)(250,2899)(251,2898)(252,2897)(253,2896)(254,2895)(255,2894)(256,2893)(257,2892)(258,2891)(259,2890)(260,2889)(261,2888)(262,2887)(263,2886)(264,2885)(265,2884)(266,2883)(267,2882)(268,2881)(269,2880)(270,2879)(271,2878)(272,2877)(273,2876)(274,2875)(275,2874)(276,2873)(277,2872)(278,2871)(279,2870)(280,2869)(281,2868)(282,2867)(283,2866)(284,2865)(285,2864)(286,2863)(287,2862)(288,2861)(289,2860)(290,2859)(291,2858)(292,2857)(293,2856)(294,2855)(295,2854)(296,2853)(297,2852)(298,2851)(299,2850)(300,2849)(301,2848)(302,2847)(303,2846)(304,2845)(305,2844)(306,2843)(307,2842)(308,2841)(309,2840)(310,2839)(311,2838)(312,2837)(313,2836)(314,2835)(315,2834)(316,2833)(317,2832)(318,2831)(319,2830)(320,2829)(321,2828)(322,2827)(323,2826)(324,2825)(325,2824)(326,2823)(327,2822)(328,2821)(329,2820)(330,2819)(331,2818)(332,2817)(333,2816)(334,2815)(335,2814)(336,2813)(337,2812)(338,2811)(339,2810)(340,2809)(341,2808)(342,2807)(343,2806)(344,2805)(345,2804)(346,2803)(347,2802)(348,2801)(349,2800)(350,2799)(351,2798)(352,2797)(353,2796)(354,2795)(355,2794)(356,2793)(357,2792)(358,2791)(359,2790)(360,2789)(361,2788)(362,2787)(363,2786)(364,2785)(365,2784)(366,2783)(367,2782)(368,2781)(369,2780)(370,2779)(371,2778)(372,2777)(373,2776)(374,2775)(375,2774)(376,2773)(377,2772)(378,2771)(379,2770)(380,2769)(381,2768)(382,2767)(383,2766)(384,2765)(385,2764)(386,2763)(387,2762)(388,2761)(389,2760)(390,2759)(391,2758)(392,2757)(393,2756)(394,2755)(395,2754)(396,2753)(397,2752)(398,2751)(399,2750)(400,2749)(401,2748)(402,2747)(403,2746)(404,2745)(405,2744)(406,2743)(407,2742)(408,2741)(409,2740)(410,2739)(411,2738)(412,2737)(413,2736)(414,2735)(415,2734)(416,2733)(417,2732)(418,2731)(419,2730)(420,2729)(421,2728)(422,2727)(423,2726)(424,2725)(425,2724)(426,2723)(427,2722)(428,2721)(429,2720)(430,2719)(431,2718)(432,2717)(433,2716)(434,2715)(435,2714)(436,2713)(437,2712)(438,2711)(439,2710)(440,2709)(441,2708)(442,2707)(443,2706)(444,2705)(445,2704)(446,2703)(447,2702)(448,2701)(449,2700)(450,2699)(451,2698)(452,2697)(453,2696)(454,2695)(455,2694)(456,2693)(457,2692)(458,2691)(459,2690)(460,2689)(461,2688)(462,2687)(463,2686)(464,2685)(465,2684)(466,2683)(467,2682)(468,2681)(469,2680)(470,2679)(471,2678)(472,2677)(473,2676)(474,2675)(475,2674)(476,2673)(477,2672)(478,2671)(479,2670)(480,2669)(481,2668)(482,2667)(483,2666)(484,2665)(485,2664)(486,2663)(487,2662)(488,2661)(489,2660)(490,2659)(491,2658)(492,2657)(493,2656)(494,2655)(495,2654)(496,2653)(497,2652)(498,2651)(499,2650)(500,2649)(501,2648)(502,2647)(503,2646)(504,2645)(505,2644)(506,2643)(507,2642)(508,2641)(509,2640)(510,2639)(511,2638)(512,2637)(513,2636)(514,2635)(515,2634)(516,2633)(517,2632)(518,2631)(519,2630)(520,2629)(521,2628)(522,2627)(523,2626)(524,2625)(525,2624)(526,2623)(527,2622)(528,2621)(529,2620)(530,2619)(531,2618)(532,2617)(533,2616)(534,2615)(535,2614)(536,2613)(537,2612)(538,2611)(539,2610)(540,2609)(541,2608)(542,2607)(543,2606)(544,2605)(545,2604)(546,2603)(547,2602)(548,2601)(549,2600)(550,2599)(551,2598)(552,2597)(553,2596)(554,2595)(555,2594)(556,2593)(557,2592)(558,2591)(559,2590)(560,2589)(561,2588)(562,2587)(563,2586)(564,2585)(565,2584)(566,2583)(567,2582)(568,2581)(569,2580)(570,2579)(571,2578)(572,2577)(573,2576)(574,2575)(575,2574)(576,2573)(577,2572)(578,2571)(579,2570)(580,2569)(581,2568)(582,2567)(583,2566)(584,2565)(585,2564)(586,2563)(587,2562)(588,2561)(589,2560)(590,2559)(591,2558)(592,2557)(593,2556)(594,2555)(595,2554)(596,2553)(597,2552)(598,2551)(599,2550)(600,2549)(601,2548)(602,2547)(603,2546)(604,2545)(605,2544)(606,2543)(607,2542)(608,2541)(609,2540)(610,2539)(611,2538)(612,2537)(613,2536)(614,2535)(615,2534)(616,2533)(617,2532)(618,2531)(619,2530)(620,2529)(621,2528)(622,2527)(623,2526)(624,2525)(625,2524)(626,2523)(627,2522)(628,2521)(629,2520)(630,2519)(631,2518)(632,2517)(633,2516)(634,2515)(635,2514)(636,2513)(637,2512)(638,2511)(639,2510)(640,2509)(641,2508)(642,2507)(643,2506)(644,2505)(645,2504)(646,2503)(647,2502)(648,2501)(649,2500)(650,2499)(651,2498)(652,2497)(653,2496)(654,2495)(655,2494)(656,2493)(657,2492)(658,2491)(659,2490)(660,2489)(661,2488)(662,2487)(663,2486)(664,2485)(665,2484)(666,2483)(667,2482)(668,2481)(669,2480)(670,2479)(671,2478)(672,2477)(673,2476)(674,2475)(675,2474)(676,2473)(677,2472)(678,2471)(679,2470)(680,2469)(681,2468)(682,2467)(683,2466)(684,2465)(685,2464)(686,2463)(687,2462)(688,2461)(689,2460)(690,2459)(691,2458)(692,2457)(693,2456)(694,2455)(695,2454)(696,2453)(697,2452)(698,2451)(699,2450)(700,2449)(701,2448)(702,2447)(703,2446)(704,2445)(705,2444)(706,2443)(707,2442)(708,2441)(709,2440)(710,2439)(711,2438)(712,2437)(713,2436)(714,2435)(715,2434)(716,2433)(717,2432)(718,2431)(719,2430)(720,2429)(721,2428)(722,2427)(723,2426)(724,2425)(725,2424)(726,2423)(727,2422)(728,2421)(729,2420)(730,2419)(731,2418)(732,2417)(733,2416)(734,2415)(735,2414)(736,2413)(737,2412)(738,2411)(739,2410)(740,2409)(741,2408)(742,2407)(743,2406)(744,2405)(745,2404)(746,2403)(747,2402)(748,2401)(749,2400)(750,2399)(751,2398)(752,2397)(753,2396)(754,2395)(755,2394)(756,2393)(757,2392)(758,2391)(759,2390)(760,2389)(761,2388)(762,2387)(763,2386)(764,2385)(765,2384)(766,2383)(767,2382)(768,2381)(769,2380)(770,2379)(771,2378)(772,2377)(773,2376)(774,2375)(775,2374)(776,2373)(777,2372)(778,2371)(779,2370)(780,2369)(781,2368)(782,2367)(783,2366)(784,2365)(785,2364)(786,2363)(787,2362)(788,2361)(789,2360)(790,2359)(791,2358)(792,2357)(793,2356)(794,2355)(795,2354)(796,2353)(797,2352)(798,2351)(799,2350)(800,2349)(801,2348)(802,2347)(803,2346)(804,2345)(805,2344)(806,2343)(807,2342)(808,2341)(809,2340)(810,2339)(811,2338)(812,2337)(813,2336)(814,2335)(815,2334)(816,2333)(817,2332)(818,2331)(819,2330)(820,2329)(821,2328)(822,2327)(823,2326)(824,2325)(825,2324)(826,2323)(827,2322)(828,2321)(829,2320)(830,2319)(831,2318)(832,2317)(833,2316)(834,2315)(835,2314)(836,2313)(837,2312)(838,2311)(839,2310)(840,2309)(841,2308)(842,2307)(843,2306)(844,2305)(845,2304)(846,2303)(847,2302)(848,2301)(849,2300)(850,2299)(851,2298)(852,2297)(853,2296)(854,2295)(855,2294)(856,2293)(857,2292)(858,2291)(859,2290)(860,2289)(861,2288)(862,2287)(863,2286)(864,2285)(865,2284)(866,2283)(867,2282)(868,2281)(869,2280)(870,2279)(871,2278)(872,2277)(873,2276)(874,2275)(875,2274)(876,2273)(877,2272)(878,2271)(879,2270)(880,2269)(881,2268)(882,2267)(883,2266)(884,2265)(885,2264)(886,2263)(887,2262)(888,2261)(889,2260)(890,2259)(891,2258)(892,2257)(893,2256)(894,2255)(895,2254)(896,2253)(897,2252)(898,2251)(899,2250)(900,2249)(901,2248)(902,2247)(903,2246)(904,2245)(905,2244)(906,2243)(907,2242)(908,2241)(909,2240)(910,2239)(911,2238)(912,2237)(913,2236)(914,2235)(915,2234)(916,2233)(917,2232)(918,2231)(919,2230)(920,2229)(921,2228)(922,2227)(923,2226)(924,2225)(925,2224)(926,2223)(927,2222)(928,2221)(929,2220)(930,2219)(931,2218)(932,2217)(933,2216)(934,2215)(935,2214)(936,2213)(937,2212)(938,2211)(939,2210)(940,2209)(941,2208)(942,2207)(943,2206)(944,2205)(945,2204)(946,2203)(947,2202)(948,2201)(949,2200)(950,2199)(951,2198)(952,2197)(953,2196)(954,2195)(955,2194)(956,2193)(957,2192)(958,2191)(959,2190)(960,2189)(961,2188)(962,2187)(963,2186)(964,2185)(965,2184)(966,2183)(967,2182)(968,2181)(969,2180)(970,2179)(971,2178)(972,2177)(973,2176)(974,2175)(975,2174)(976,2173)(977,2172)(978,2171)(979,2170)(980,2169)(981,2168)(982,2167)(983,2166)(984,2165)(985,2164)(986,2163)(987,2162)(988,2161)(989,2160)(990,2159)(991,2158)(992,2157)(993,2156)(994,2155)(995,2154)(996,2153)(997,2152)(998,2151)(999,2150)(1000,2149)(1001,2148)(1002,2147)(1003,2146)(1004,2145)(1005,2144)(1006,2143)(1007,2142)(1008,2141)(1009,2140)(1010,2139)(1011,2138)(1012,2137)(1013,2136)(1014,2135)(1015,2134)(1016,2133)(1017,2132)(1018,2131)(1019,2130)(1020,2129)(1021,2128)(1022,2127)(1023,2126)(1024,2125)(1025,2124)(1026,2123)(1027,2122)(1028,2121)(1029,2120)(1030,2119)(1031,2118)(1032,2117)(1033,2116)(1034,2115)(1035,2114)(1036,2113)(1037,2112)(1038,2111)(1039,2110)(1040,2109)(1041,2108)(1042,2107)(1043,2106)(1044,2105)(1045,2104)(1046,2103)(1047,2102)(1048,2101)(1049,2100)(1050,2099)(1051,2098)(1052,2097)(1053,2096)(1054,2095)(1055,2094)(1056,2093)(1057,2092)(1058,2091)(1059,2090)(1060,2089)(1061,2088)(1062,2087)(1063,2086)(1064,2085)(1065,2084)(1066,2083)(1067,2082)(1068,2081)(1069,2080)(1070,2079)(1071,2078)(1072,2077)(1073,2076)(1074,2075)(1075,2074)(1076,2073)(1077,2072)(1078,2071)(1079,2070)(1080,2069)(1081,2068)(1082,2067)(1083,2066)(1084,2065)(1085,2064)(1086,2063)(1087,2062)(1088,2061)(1089,2060)(1090,2059)(1091,2058)(1092,2057)(1093,2056)(1094,2055)(1095,2054)(1096,2053)(1097,2052)(1098,2051)(1099,2050)(1100,2049)(1101,2048)(1102,2047)(1103,2046)(1104,2045)(1105,2044)(1106,2043)(1107,2042)(1108,2041)(1109,2040)(1110,2039)(1111,2038)(1112,2037)(1113,2036)(1114,2035)(1115,2034)(1116,2033)(1117,2032)(1118,2031)(1119,2030)(1120,2029)(1121,2028)(1122,2027)(1123,2026)(1124,2025)(1125,2024)(1126,2023)(1127,2022)(1128,2021)(1129,2020)(1130,2019)(1131,2018)(1132,2017)(1133,2016)(1134,2015)(1135,2014)(1136,2013)(1137,2012)(1138,2011)(1139,2010)(1140,2009)(1141,2008)(1142,2007)(1143,2006)(1144,2005)(1145,2004)(1146,2003)(1147,2002)(1148,2001)(1149,2000)(1150,1999)(1151,1998)(1152,1997)(1153,1996)(1154,1995)(1155,1994)(1156,1993)(1157,1992)(1158,1991)(1159,1990)(1160,1989)(1161,1988)(1162,1987)(1163,1986)(1164,1985)(1165,1984)(1166,1983)(1167,1982)(1168,1981)(1169,1980)(1170,1979)(1171,1978)(1172,1977)(1173,1976)(1174,1975)(1175,1974)(1176,1973)(1177,1972)(1178,1971)(1179,1970)(1180,1969)(1181,1968)(1182,1967)(1183,1966)(1184,1965)(1185,1964)(1186,1963)(1187,1962)(1188,1961)(1189,1960)(1190,1959)(1191,1958)(1192,1957)(1193,1956)(1194,1955)(1195,1954)(1196,1953)(1197,1952)(1198,1951)(1199,1950)(1200,1949)(1201,1948)(1202,1947)(1203,1946)(1204,1945)(1205,1944)(1206,1943)(1207,1942)(1208,1941)(1209,1940)(1210,1939)(1211,1938)(1212,1937)(1213,1936)(1214,1935)(1215,1934)(1216,1933)(1217,1932)(1218,1931)(1219,1930)(1220,1929)(1221,1928)(1222,1927)(1223,1926)(1224,1925)(1225,1924)(1226,1923)(1227,1922)(1228,1921)(1229,1920)(1230,1919)(1231,1918)(1232,1917)(1233,1916)(1234,1915)(1235,1914)(1236,1913)(1237,1912)(1238,1911)(1239,1910)(1240,1909)(1241,1908)(1242,1907)(1243,1906)(1244,1905)(1245,1904)(1246,1903)(1247,1902)(1248,1901)(1249,1900)(1250,1899)(1251,1898)(1252,1897)(1253,1896)(1254,1895)(1255,1894)(1256,1893)(1257,1892)(1258,1891)(1259,1890)(1260,1889)(1261,1888)(1262,1887)(1263,1886)(1264,1885)(1265,1884)(1266,1883)(1267,1882)(1268,1881)(1269,1880)(1270,1879)(1271,1878)(1272,1877)(1273,1876)(1274,1875)(1275,1874)(1276,1873)(1277,1872)(1278,1871)(1279,1870)(1280,1869)(1281,1868)(1282,1867)(1283,1866)(1284,1865)(1285,1864)(1286,1863)(1287,1862)(1288,1861)(1289,1860)(1290,1859)(1291,1858)(1292,1857)(1293,1856)(1294,1855)(1295,1854)(1296,1853)(1297,1852)(1298,1851)(1299,1850)(1300,1849)(1301,1848)(1302,1847)(1303,1846)(1304,1845)(1305,1844)(1306,1843)(1307,1842)(1308,1841)(1309,1840)(1310,1839)(1311,1838)(1312,1837)(1313,1836)(1314,1835)(1315,1834)(1316,1833)(1317,1832)(1318,1831)(1319,1830)(1320,1829)(1321,1828)(1322,1827)(1323,1826)(1324,1825)(1325,1824)(1326,1823)(1327,1822)(1328,1821)(1329,1820)(1330,1819)(1331,1818)(1332,1817)(1333,1816)(1334,1815)(1335,1814)(1336,1813)(1337,1812)(1338,1811)(1339,1810)(1340,1809)(1341,1808)(1342,1807)(1343,1806)(1344,1805)(1345,1804)(1346,1803)(1347,1802)(1348,1801)(1349,1800)(1350,1799)(1351,1798)(1352,1797)(1353,1796)(1354,1795)(1355,1794)(1356,1793)(1357,1792)(1358,1791)(1359,1790)(1360,1789)(1361,1788)(1362,1787)(1363,1786)(1364,1785)(1365,1784)(1366,1783)(1367,1782)(1368,1781)(1369,1780)(1370,1779)(1371,1778)(1372,1777)(1373,1776)(1374,1775)(1375,1774)(1376,1773)(1377,1772)(1378,1771)(1379,1770)(1380,1769)(1381,1768)(1382,1767)(1383,1766)(1384,1765)(1385,1764)(1386,1763)(1387,1762)(1388,1761)(1389,1760)(1390,1759)(1391,1758)(1392,1757)(1393,1756)(1394,1755)(1395,1754)(1396,1753)(1397,1752)(1398,1751)(1399,1750)(1400,1749)(1401,1748)(1402,1747)(1403,1746)(1404,1745)(1405,1744)(1406,1743)(1407,1742)(1408,1741)(1409,1740)(1410,1739)(1411,1738)(1412,1737)(1413,1736)(1414,1735)(1415,1734)(1416,1733)(1417,1732)(1418,1731)(1419,1730)(1420,1729)(1421,1728)(1422,1727)(1423,1726)(1424,1725)(1425,1724)(1426,1723)(1427,1722)(1428,1721)(1429,1720)(1430,1719)(1431,1718)(1432,1717)(1433,1716)(1434,1715)(1435,1714)(1436,1713)(1437,1712)(1438,1711)(1439,1710)(1440,1709)(1441,1708)(1442,1707)(1443,1706)(1444,1705)(1445,1704)(1446,1703)(1447,1702)(1448,1701)(1449,1700)(1450,1699)(1451,1698)(1452,1697)(1453,1696)(1454,1695)(1455,1694)(1456,1693)(1457,1692)(1458,1691)(1459,1690)(1460,1689)(1461,1688)(1462,1687)(1463,1686)(1464,1685)(1465,1684)(1466,1683)(1467,1682)(1468,1681)(1469,1680)(1470,1679)(1471,1678)(1472,1677)(1473,1676)(1474,1675)(1475,1674)(1476,1673)(1477,1672)(1478,1671)(1479,1670)(1480,1669)(1481,1668)(1482,1667)(1483,1666)(1484,1665)(1485,1664)(1486,1663)(1487,1662)(1488,1661)(1489,1660)(1490,1659)(1491,1658)(1492,1657)(1493,1656)(1494,1655)(1495,1654)(1496,1653)(1497,1652)(1498,1651)(1499,1650)(1500,1649)(1501,1648)(1502,1647)(1503,1646)(1504,1645)(1505,1644)(1506,1643)(1507,1642)(1508,1641)(1509,1640)(1510,1639)(1511,1638)(1512,1637)(1513,1636)(1514,1635)(1515,1634)(1516,1633)(1517,1632)(1518,1631)(1519,1630)(1520,1629)(1521,1628)(1522,1627)(1523,1626)(1524,1625)(1525,1624)(1526,1623)(1527,1622)(1528,1621)(1529,1620)(1530,1619)(1531,1618)(1532,1617)(1533,1616)(1534,1615)(1535,1614)(1536,1613)(1537,1612)(1538,1611)(1539,1610)(1540,1609)(1541,1608)(1542,1607)(1543,1606)(1544,1605)(1545,1604)(1546,1603)(1547,1602)(1548,1601)(1549,1600)(1550,1599)(1551,1598)(1552,1597)(1553,1596)(1554,1595)(1555,1594)(1556,1593)(1557,1592)(1558,1591)(1559,1590)(1560,1589)(1561,1588)(1562,1587)(1563,1586)(1564,1585)(1565,1584)(1566,1583)(1567,1582)(1568,1581)(1569,1580)(1570,1579)(1571,1578)(1572,1577)(1573,1576)(1574,1575)
Polycyclic presentation:
2,5,3137|b^a=b^4,c^a=c^3136
Conjugacy classes & character table
7844 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31370, 3);
Finite Group Databasebeta