← Prev (#44527293) Next (#44527295) →
D15545 #44527294
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3114 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);(2,5)(3,4)(7,3114)(8,3113)(9,3112)(10,3111)(11,3110)(12,3109)(13,3108)(14,3107)(15,3106)(16,3105)(17,3104)(18,3103)(19,3102)(20,3101)(21,3100)(22,3099)(23,3098)(24,3097)(25,3096)(26,3095)(27,3094)(28,3093)(29,3092)(30,3091)(31,3090)(32,3089)(33,3088)(34,3087)(35,3086)(36,3085)(37,3084)(38,3083)(39,3082)(40,3081)(41,3080)(42,3079)(43,3078)(44,3077)(45,3076)(46,3075)(47,3074)(48,3073)(49,3072)(50,3071)(51,3070)(52,3069)(53,3068)(54,3067)(55,3066)(56,3065)(57,3064)(58,3063)(59,3062)(60,3061)(61,3060)(62,3059)(63,3058)(64,3057)(65,3056)(66,3055)(67,3054)(68,3053)(69,3052)(70,3051)(71,3050)(72,3049)(73,3048)(74,3047)(75,3046)(76,3045)(77,3044)(78,3043)(79,3042)(80,3041)(81,3040)(82,3039)(83,3038)(84,3037)(85,3036)(86,3035)(87,3034)(88,3033)(89,3032)(90,3031)(91,3030)(92,3029)(93,3028)(94,3027)(95,3026)(96,3025)(97,3024)(98,3023)(99,3022)(100,3021)(101,3020)(102,3019)(103,3018)(104,3017)(105,3016)(106,3015)(107,3014)(108,3013)(109,3012)(110,3011)(111,3010)(112,3009)(113,3008)(114,3007)(115,3006)(116,3005)(117,3004)(118,3003)(119,3002)(120,3001)(121,3000)(122,2999)(123,2998)(124,2997)(125,2996)(126,2995)(127,2994)(128,2993)(129,2992)(130,2991)(131,2990)(132,2989)(133,2988)(134,2987)(135,2986)(136,2985)(137,2984)(138,2983)(139,2982)(140,2981)(141,2980)(142,2979)(143,2978)(144,2977)(145,2976)(146,2975)(147,2974)(148,2973)(149,2972)(150,2971)(151,2970)(152,2969)(153,2968)(154,2967)(155,2966)(156,2965)(157,2964)(158,2963)(159,2962)(160,2961)(161,2960)(162,2959)(163,2958)(164,2957)(165,2956)(166,2955)(167,2954)(168,2953)(169,2952)(170,2951)(171,2950)(172,2949)(173,2948)(174,2947)(175,2946)(176,2945)(177,2944)(178,2943)(179,2942)(180,2941)(181,2940)(182,2939)(183,2938)(184,2937)(185,2936)(186,2935)(187,2934)(188,2933)(189,2932)(190,2931)(191,2930)(192,2929)(193,2928)(194,2927)(195,2926)(196,2925)(197,2924)(198,2923)(199,2922)(200,2921)(201,2920)(202,2919)(203,2918)(204,2917)(205,2916)(206,2915)(207,2914)(208,2913)(209,2912)(210,2911)(211,2910)(212,2909)(213,2908)(214,2907)(215,2906)(216,2905)(217,2904)(218,2903)(219,2902)(220,2901)(221,2900)(222,2899)(223,2898)(224,2897)(225,2896)(226,2895)(227,2894)(228,2893)(229,2892)(230,2891)(231,2890)(232,2889)(233,2888)(234,2887)(235,2886)(236,2885)(237,2884)(238,2883)(239,2882)(240,2881)(241,2880)(242,2879)(243,2878)(244,2877)(245,2876)(246,2875)(247,2874)(248,2873)(249,2872)(250,2871)(251,2870)(252,2869)(253,2868)(254,2867)(255,2866)(256,2865)(257,2864)(258,2863)(259,2862)(260,2861)(261,2860)(262,2859)(263,2858)(264,2857)(265,2856)(266,2855)(267,2854)(268,2853)(269,2852)(270,2851)(271,2850)(272,2849)(273,2848)(274,2847)(275,2846)(276,2845)(277,2844)(278,2843)(279,2842)(280,2841)(281,2840)(282,2839)(283,2838)(284,2837)(285,2836)(286,2835)(287,2834)(288,2833)(289,2832)(290,2831)(291,2830)(292,2829)(293,2828)(294,2827)(295,2826)(296,2825)(297,2824)(298,2823)(299,2822)(300,2821)(301,2820)(302,2819)(303,2818)(304,2817)(305,2816)(306,2815)(307,2814)(308,2813)(309,2812)(310,2811)(311,2810)(312,2809)(313,2808)(314,2807)(315,2806)(316,2805)(317,2804)(318,2803)(319,2802)(320,2801)(321,2800)(322,2799)(323,2798)(324,2797)(325,2796)(326,2795)(327,2794)(328,2793)(329,2792)(330,2791)(331,2790)(332,2789)(333,2788)(334,2787)(335,2786)(336,2785)(337,2784)(338,2783)(339,2782)(340,2781)(341,2780)(342,2779)(343,2778)(344,2777)(345,2776)(346,2775)(347,2774)(348,2773)(349,2772)(350,2771)(351,2770)(352,2769)(353,2768)(354,2767)(355,2766)(356,2765)(357,2764)(358,2763)(359,2762)(360,2761)(361,2760)(362,2759)(363,2758)(364,2757)(365,2756)(366,2755)(367,2754)(368,2753)(369,2752)(370,2751)(371,2750)(372,2749)(373,2748)(374,2747)(375,2746)(376,2745)(377,2744)(378,2743)(379,2742)(380,2741)(381,2740)(382,2739)(383,2738)(384,2737)(385,2736)(386,2735)(387,2734)(388,2733)(389,2732)(390,2731)(391,2730)(392,2729)(393,2728)(394,2727)(395,2726)(396,2725)(397,2724)(398,2723)(399,2722)(400,2721)(401,2720)(402,2719)(403,2718)(404,2717)(405,2716)(406,2715)(407,2714)(408,2713)(409,2712)(410,2711)(411,2710)(412,2709)(413,2708)(414,2707)(415,2706)(416,2705)(417,2704)(418,2703)(419,2702)(420,2701)(421,2700)(422,2699)(423,2698)(424,2697)(425,2696)(426,2695)(427,2694)(428,2693)(429,2692)(430,2691)(431,2690)(432,2689)(433,2688)(434,2687)(435,2686)(436,2685)(437,2684)(438,2683)(439,2682)(440,2681)(441,2680)(442,2679)(443,2678)(444,2677)(445,2676)(446,2675)(447,2674)(448,2673)(449,2672)(450,2671)(451,2670)(452,2669)(453,2668)(454,2667)(455,2666)(456,2665)(457,2664)(458,2663)(459,2662)(460,2661)(461,2660)(462,2659)(463,2658)(464,2657)(465,2656)(466,2655)(467,2654)(468,2653)(469,2652)(470,2651)(471,2650)(472,2649)(473,2648)(474,2647)(475,2646)(476,2645)(477,2644)(478,2643)(479,2642)(480,2641)(481,2640)(482,2639)(483,2638)(484,2637)(485,2636)(486,2635)(487,2634)(488,2633)(489,2632)(490,2631)(491,2630)(492,2629)(493,2628)(494,2627)(495,2626)(496,2625)(497,2624)(498,2623)(499,2622)(500,2621)(501,2620)(502,2619)(503,2618)(504,2617)(505,2616)(506,2615)(507,2614)(508,2613)(509,2612)(510,2611)(511,2610)(512,2609)(513,2608)(514,2607)(515,2606)(516,2605)(517,2604)(518,2603)(519,2602)(520,2601)(521,2600)(522,2599)(523,2598)(524,2597)(525,2596)(526,2595)(527,2594)(528,2593)(529,2592)(530,2591)(531,2590)(532,2589)(533,2588)(534,2587)(535,2586)(536,2585)(537,2584)(538,2583)(539,2582)(540,2581)(541,2580)(542,2579)(543,2578)(544,2577)(545,2576)(546,2575)(547,2574)(548,2573)(549,2572)(550,2571)(551,2570)(552,2569)(553,2568)(554,2567)(555,2566)(556,2565)(557,2564)(558,2563)(559,2562)(560,2561)(561,2560)(562,2559)(563,2558)(564,2557)(565,2556)(566,2555)(567,2554)(568,2553)(569,2552)(570,2551)(571,2550)(572,2549)(573,2548)(574,2547)(575,2546)(576,2545)(577,2544)(578,2543)(579,2542)(580,2541)(581,2540)(582,2539)(583,2538)(584,2537)(585,2536)(586,2535)(587,2534)(588,2533)(589,2532)(590,2531)(591,2530)(592,2529)(593,2528)(594,2527)(595,2526)(596,2525)(597,2524)(598,2523)(599,2522)(600,2521)(601,2520)(602,2519)(603,2518)(604,2517)(605,2516)(606,2515)(607,2514)(608,2513)(609,2512)(610,2511)(611,2510)(612,2509)(613,2508)(614,2507)(615,2506)(616,2505)(617,2504)(618,2503)(619,2502)(620,2501)(621,2500)(622,2499)(623,2498)(624,2497)(625,2496)(626,2495)(627,2494)(628,2493)(629,2492)(630,2491)(631,2490)(632,2489)(633,2488)(634,2487)(635,2486)(636,2485)(637,2484)(638,2483)(639,2482)(640,2481)(641,2480)(642,2479)(643,2478)(644,2477)(645,2476)(646,2475)(647,2474)(648,2473)(649,2472)(650,2471)(651,2470)(652,2469)(653,2468)(654,2467)(655,2466)(656,2465)(657,2464)(658,2463)(659,2462)(660,2461)(661,2460)(662,2459)(663,2458)(664,2457)(665,2456)(666,2455)(667,2454)(668,2453)(669,2452)(670,2451)(671,2450)(672,2449)(673,2448)(674,2447)(675,2446)(676,2445)(677,2444)(678,2443)(679,2442)(680,2441)(681,2440)(682,2439)(683,2438)(684,2437)(685,2436)(686,2435)(687,2434)(688,2433)(689,2432)(690,2431)(691,2430)(692,2429)(693,2428)(694,2427)(695,2426)(696,2425)(697,2424)(698,2423)(699,2422)(700,2421)(701,2420)(702,2419)(703,2418)(704,2417)(705,2416)(706,2415)(707,2414)(708,2413)(709,2412)(710,2411)(711,2410)(712,2409)(713,2408)(714,2407)(715,2406)(716,2405)(717,2404)(718,2403)(719,2402)(720,2401)(721,2400)(722,2399)(723,2398)(724,2397)(725,2396)(726,2395)(727,2394)(728,2393)(729,2392)(730,2391)(731,2390)(732,2389)(733,2388)(734,2387)(735,2386)(736,2385)(737,2384)(738,2383)(739,2382)(740,2381)(741,2380)(742,2379)(743,2378)(744,2377)(745,2376)(746,2375)(747,2374)(748,2373)(749,2372)(750,2371)(751,2370)(752,2369)(753,2368)(754,2367)(755,2366)(756,2365)(757,2364)(758,2363)(759,2362)(760,2361)(761,2360)(762,2359)(763,2358)(764,2357)(765,2356)(766,2355)(767,2354)(768,2353)(769,2352)(770,2351)(771,2350)(772,2349)(773,2348)(774,2347)(775,2346)(776,2345)(777,2344)(778,2343)(779,2342)(780,2341)(781,2340)(782,2339)(783,2338)(784,2337)(785,2336)(786,2335)(787,2334)(788,2333)(789,2332)(790,2331)(791,2330)(792,2329)(793,2328)(794,2327)(795,2326)(796,2325)(797,2324)(798,2323)(799,2322)(800,2321)(801,2320)(802,2319)(803,2318)(804,2317)(805,2316)(806,2315)(807,2314)(808,2313)(809,2312)(810,2311)(811,2310)(812,2309)(813,2308)(814,2307)(815,2306)(816,2305)(817,2304)(818,2303)(819,2302)(820,2301)(821,2300)(822,2299)(823,2298)(824,2297)(825,2296)(826,2295)(827,2294)(828,2293)(829,2292)(830,2291)(831,2290)(832,2289)(833,2288)(834,2287)(835,2286)(836,2285)(837,2284)(838,2283)(839,2282)(840,2281)(841,2280)(842,2279)(843,2278)(844,2277)(845,2276)(846,2275)(847,2274)(848,2273)(849,2272)(850,2271)(851,2270)(852,2269)(853,2268)(854,2267)(855,2266)(856,2265)(857,2264)(858,2263)(859,2262)(860,2261)(861,2260)(862,2259)(863,2258)(864,2257)(865,2256)(866,2255)(867,2254)(868,2253)(869,2252)(870,2251)(871,2250)(872,2249)(873,2248)(874,2247)(875,2246)(876,2245)(877,2244)(878,2243)(879,2242)(880,2241)(881,2240)(882,2239)(883,2238)(884,2237)(885,2236)(886,2235)(887,2234)(888,2233)(889,2232)(890,2231)(891,2230)(892,2229)(893,2228)(894,2227)(895,2226)(896,2225)(897,2224)(898,2223)(899,2222)(900,2221)(901,2220)(902,2219)(903,2218)(904,2217)(905,2216)(906,2215)(907,2214)(908,2213)(909,2212)(910,2211)(911,2210)(912,2209)(913,2208)(914,2207)(915,2206)(916,2205)(917,2204)(918,2203)(919,2202)(920,2201)(921,2200)(922,2199)(923,2198)(924,2197)(925,2196)(926,2195)(927,2194)(928,2193)(929,2192)(930,2191)(931,2190)(932,2189)(933,2188)(934,2187)(935,2186)(936,2185)(937,2184)(938,2183)(939,2182)(940,2181)(941,2180)(942,2179)(943,2178)(944,2177)(945,2176)(946,2175)(947,2174)(948,2173)(949,2172)(950,2171)(951,2170)(952,2169)(953,2168)(954,2167)(955,2166)(956,2165)(957,2164)(958,2163)(959,2162)(960,2161)(961,2160)(962,2159)(963,2158)(964,2157)(965,2156)(966,2155)(967,2154)(968,2153)(969,2152)(970,2151)(971,2150)(972,2149)(973,2148)(974,2147)(975,2146)(976,2145)(977,2144)(978,2143)(979,2142)(980,2141)(981,2140)(982,2139)(983,2138)(984,2137)(985,2136)(986,2135)(987,2134)(988,2133)(989,2132)(990,2131)(991,2130)(992,2129)(993,2128)(994,2127)(995,2126)(996,2125)(997,2124)(998,2123)(999,2122)(1000,2121)(1001,2120)(1002,2119)(1003,2118)(1004,2117)(1005,2116)(1006,2115)(1007,2114)(1008,2113)(1009,2112)(1010,2111)(1011,2110)(1012,2109)(1013,2108)(1014,2107)(1015,2106)(1016,2105)(1017,2104)(1018,2103)(1019,2102)(1020,2101)(1021,2100)(1022,2099)(1023,2098)(1024,2097)(1025,2096)(1026,2095)(1027,2094)(1028,2093)(1029,2092)(1030,2091)(1031,2090)(1032,2089)(1033,2088)(1034,2087)(1035,2086)(1036,2085)(1037,2084)(1038,2083)(1039,2082)(1040,2081)(1041,2080)(1042,2079)(1043,2078)(1044,2077)(1045,2076)(1046,2075)(1047,2074)(1048,2073)(1049,2072)(1050,2071)(1051,2070)(1052,2069)(1053,2068)(1054,2067)(1055,2066)(1056,2065)(1057,2064)(1058,2063)(1059,2062)(1060,2061)(1061,2060)(1062,2059)(1063,2058)(1064,2057)(1065,2056)(1066,2055)(1067,2054)(1068,2053)(1069,2052)(1070,2051)(1071,2050)(1072,2049)(1073,2048)(1074,2047)(1075,2046)(1076,2045)(1077,2044)(1078,2043)(1079,2042)(1080,2041)(1081,2040)(1082,2039)(1083,2038)(1084,2037)(1085,2036)(1086,2035)(1087,2034)(1088,2033)(1089,2032)(1090,2031)(1091,2030)(1092,2029)(1093,2028)(1094,2027)(1095,2026)(1096,2025)(1097,2024)(1098,2023)(1099,2022)(1100,2021)(1101,2020)(1102,2019)(1103,2018)(1104,2017)(1105,2016)(1106,2015)(1107,2014)(1108,2013)(1109,2012)(1110,2011)(1111,2010)(1112,2009)(1113,2008)(1114,2007)(1115,2006)(1116,2005)(1117,2004)(1118,2003)(1119,2002)(1120,2001)(1121,2000)(1122,1999)(1123,1998)(1124,1997)(1125,1996)(1126,1995)(1127,1994)(1128,1993)(1129,1992)(1130,1991)(1131,1990)(1132,1989)(1133,1988)(1134,1987)(1135,1986)(1136,1985)(1137,1984)(1138,1983)(1139,1982)(1140,1981)(1141,1980)(1142,1979)(1143,1978)(1144,1977)(1145,1976)(1146,1975)(1147,1974)(1148,1973)(1149,1972)(1150,1971)(1151,1970)(1152,1969)(1153,1968)(1154,1967)(1155,1966)(1156,1965)(1157,1964)(1158,1963)(1159,1962)(1160,1961)(1161,1960)(1162,1959)(1163,1958)(1164,1957)(1165,1956)(1166,1955)(1167,1954)(1168,1953)(1169,1952)(1170,1951)(1171,1950)(1172,1949)(1173,1948)(1174,1947)(1175,1946)(1176,1945)(1177,1944)(1178,1943)(1179,1942)(1180,1941)(1181,1940)(1182,1939)(1183,1938)(1184,1937)(1185,1936)(1186,1935)(1187,1934)(1188,1933)(1189,1932)(1190,1931)(1191,1930)(1192,1929)(1193,1928)(1194,1927)(1195,1926)(1196,1925)(1197,1924)(1198,1923)(1199,1922)(1200,1921)(1201,1920)(1202,1919)(1203,1918)(1204,1917)(1205,1916)(1206,1915)(1207,1914)(1208,1913)(1209,1912)(1210,1911)(1211,1910)(1212,1909)(1213,1908)(1214,1907)(1215,1906)(1216,1905)(1217,1904)(1218,1903)(1219,1902)(1220,1901)(1221,1900)(1222,1899)(1223,1898)(1224,1897)(1225,1896)(1226,1895)(1227,1894)(1228,1893)(1229,1892)(1230,1891)(1231,1890)(1232,1889)(1233,1888)(1234,1887)(1235,1886)(1236,1885)(1237,1884)(1238,1883)(1239,1882)(1240,1881)(1241,1880)(1242,1879)(1243,1878)(1244,1877)(1245,1876)(1246,1875)(1247,1874)(1248,1873)(1249,1872)(1250,1871)(1251,1870)(1252,1869)(1253,1868)(1254,1867)(1255,1866)(1256,1865)(1257,1864)(1258,1863)(1259,1862)(1260,1861)(1261,1860)(1262,1859)(1263,1858)(1264,1857)(1265,1856)(1266,1855)(1267,1854)(1268,1853)(1269,1852)(1270,1851)(1271,1850)(1272,1849)(1273,1848)(1274,1847)(1275,1846)(1276,1845)(1277,1844)(1278,1843)(1279,1842)(1280,1841)(1281,1840)(1282,1839)(1283,1838)(1284,1837)(1285,1836)(1286,1835)(1287,1834)(1288,1833)(1289,1832)(1290,1831)(1291,1830)(1292,1829)(1293,1828)(1294,1827)(1295,1826)(1296,1825)(1297,1824)(1298,1823)(1299,1822)(1300,1821)(1301,1820)(1302,1819)(1303,1818)(1304,1817)(1305,1816)(1306,1815)(1307,1814)(1308,1813)(1309,1812)(1310,1811)(1311,1810)(1312,1809)(1313,1808)(1314,1807)(1315,1806)(1316,1805)(1317,1804)(1318,1803)(1319,1802)(1320,1801)(1321,1800)(1322,1799)(1323,1798)(1324,1797)(1325,1796)(1326,1795)(1327,1794)(1328,1793)(1329,1792)(1330,1791)(1331,1790)(1332,1789)(1333,1788)(1334,1787)(1335,1786)(1336,1785)(1337,1784)(1338,1783)(1339,1782)(1340,1781)(1341,1780)(1342,1779)(1343,1778)(1344,1777)(1345,1776)(1346,1775)(1347,1774)(1348,1773)(1349,1772)(1350,1771)(1351,1770)(1352,1769)(1353,1768)(1354,1767)(1355,1766)(1356,1765)(1357,1764)(1358,1763)(1359,1762)(1360,1761)(1361,1760)(1362,1759)(1363,1758)(1364,1757)(1365,1756)(1366,1755)(1367,1754)(1368,1753)(1369,1752)(1370,1751)(1371,1750)(1372,1749)(1373,1748)(1374,1747)(1375,1746)(1376,1745)(1377,1744)(1378,1743)(1379,1742)(1380,1741)(1381,1740)(1382,1739)(1383,1738)(1384,1737)(1385,1736)(1386,1735)(1387,1734)(1388,1733)(1389,1732)(1390,1731)(1391,1730)(1392,1729)(1393,1728)(1394,1727)(1395,1726)(1396,1725)(1397,1724)(1398,1723)(1399,1722)(1400,1721)(1401,1720)(1402,1719)(1403,1718)(1404,1717)(1405,1716)(1406,1715)(1407,1714)(1408,1713)(1409,1712)(1410,1711)(1411,1710)(1412,1709)(1413,1708)(1414,1707)(1415,1706)(1416,1705)(1417,1704)(1418,1703)(1419,1702)(1420,1701)(1421,1700)(1422,1699)(1423,1698)(1424,1697)(1425,1696)(1426,1695)(1427,1694)(1428,1693)(1429,1692)(1430,1691)(1431,1690)(1432,1689)(1433,1688)(1434,1687)(1435,1686)(1436,1685)(1437,1684)(1438,1683)(1439,1682)(1440,1681)(1441,1680)(1442,1679)(1443,1678)(1444,1677)(1445,1676)(1446,1675)(1447,1674)(1448,1673)(1449,1672)(1450,1671)(1451,1670)(1452,1669)(1453,1668)(1454,1667)(1455,1666)(1456,1665)(1457,1664)(1458,1663)(1459,1662)(1460,1661)(1461,1660)(1462,1659)(1463,1658)(1464,1657)(1465,1656)(1466,1655)(1467,1654)(1468,1653)(1469,1652)(1470,1651)(1471,1650)(1472,1649)(1473,1648)(1474,1647)(1475,1646)(1476,1645)(1477,1644)(1478,1643)(1479,1642)(1480,1641)(1481,1640)(1482,1639)(1483,1638)(1484,1637)(1485,1636)(1486,1635)(1487,1634)(1488,1633)(1489,1632)(1490,1631)(1491,1630)(1492,1629)(1493,1628)(1494,1627)(1495,1626)(1496,1625)(1497,1624)(1498,1623)(1499,1622)(1500,1621)(1501,1620)(1502,1619)(1503,1618)(1504,1617)(1505,1616)(1506,1615)(1507,1614)(1508,1613)(1509,1612)(1510,1611)(1511,1610)(1512,1609)(1513,1608)(1514,1607)(1515,1606)(1516,1605)(1517,1604)(1518,1603)(1519,1602)(1520,1601)(1521,1600)(1522,1599)(1523,1598)(1524,1597)(1525,1596)(1526,1595)(1527,1594)(1528,1593)(1529,1592)(1530,1591)(1531,1590)(1532,1589)(1533,1588)(1534,1587)(1535,1586)(1536,1585)(1537,1584)(1538,1583)(1539,1582)(1540,1581)(1541,1580)(1542,1579)(1543,1578)(1544,1577)(1545,1576)(1546,1575)(1547,1574)(1548,1573)(1549,1572)(1550,1571)(1551,1570)(1552,1569)(1553,1568)(1554,1567)(1555,1566)(1556,1565)(1557,1564)(1558,1563)(1559,1562)(1560,1561)
Polycyclic presentation:
2,5,3109|b^a=b^4,c^a=c^3108
Conjugacy classes & character table
7774 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31090, 3);
Finite Group Databasebeta