← Prev (#44499481) Next (#44499483) →
D15305 #44499482
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3066 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);(2,5)(3,4)(7,3066)(8,3065)(9,3064)(10,3063)(11,3062)(12,3061)(13,3060)(14,3059)(15,3058)(16,3057)(17,3056)(18,3055)(19,3054)(20,3053)(21,3052)(22,3051)(23,3050)(24,3049)(25,3048)(26,3047)(27,3046)(28,3045)(29,3044)(30,3043)(31,3042)(32,3041)(33,3040)(34,3039)(35,3038)(36,3037)(37,3036)(38,3035)(39,3034)(40,3033)(41,3032)(42,3031)(43,3030)(44,3029)(45,3028)(46,3027)(47,3026)(48,3025)(49,3024)(50,3023)(51,3022)(52,3021)(53,3020)(54,3019)(55,3018)(56,3017)(57,3016)(58,3015)(59,3014)(60,3013)(61,3012)(62,3011)(63,3010)(64,3009)(65,3008)(66,3007)(67,3006)(68,3005)(69,3004)(70,3003)(71,3002)(72,3001)(73,3000)(74,2999)(75,2998)(76,2997)(77,2996)(78,2995)(79,2994)(80,2993)(81,2992)(82,2991)(83,2990)(84,2989)(85,2988)(86,2987)(87,2986)(88,2985)(89,2984)(90,2983)(91,2982)(92,2981)(93,2980)(94,2979)(95,2978)(96,2977)(97,2976)(98,2975)(99,2974)(100,2973)(101,2972)(102,2971)(103,2970)(104,2969)(105,2968)(106,2967)(107,2966)(108,2965)(109,2964)(110,2963)(111,2962)(112,2961)(113,2960)(114,2959)(115,2958)(116,2957)(117,2956)(118,2955)(119,2954)(120,2953)(121,2952)(122,2951)(123,2950)(124,2949)(125,2948)(126,2947)(127,2946)(128,2945)(129,2944)(130,2943)(131,2942)(132,2941)(133,2940)(134,2939)(135,2938)(136,2937)(137,2936)(138,2935)(139,2934)(140,2933)(141,2932)(142,2931)(143,2930)(144,2929)(145,2928)(146,2927)(147,2926)(148,2925)(149,2924)(150,2923)(151,2922)(152,2921)(153,2920)(154,2919)(155,2918)(156,2917)(157,2916)(158,2915)(159,2914)(160,2913)(161,2912)(162,2911)(163,2910)(164,2909)(165,2908)(166,2907)(167,2906)(168,2905)(169,2904)(170,2903)(171,2902)(172,2901)(173,2900)(174,2899)(175,2898)(176,2897)(177,2896)(178,2895)(179,2894)(180,2893)(181,2892)(182,2891)(183,2890)(184,2889)(185,2888)(186,2887)(187,2886)(188,2885)(189,2884)(190,2883)(191,2882)(192,2881)(193,2880)(194,2879)(195,2878)(196,2877)(197,2876)(198,2875)(199,2874)(200,2873)(201,2872)(202,2871)(203,2870)(204,2869)(205,2868)(206,2867)(207,2866)(208,2865)(209,2864)(210,2863)(211,2862)(212,2861)(213,2860)(214,2859)(215,2858)(216,2857)(217,2856)(218,2855)(219,2854)(220,2853)(221,2852)(222,2851)(223,2850)(224,2849)(225,2848)(226,2847)(227,2846)(228,2845)(229,2844)(230,2843)(231,2842)(232,2841)(233,2840)(234,2839)(235,2838)(236,2837)(237,2836)(238,2835)(239,2834)(240,2833)(241,2832)(242,2831)(243,2830)(244,2829)(245,2828)(246,2827)(247,2826)(248,2825)(249,2824)(250,2823)(251,2822)(252,2821)(253,2820)(254,2819)(255,2818)(256,2817)(257,2816)(258,2815)(259,2814)(260,2813)(261,2812)(262,2811)(263,2810)(264,2809)(265,2808)(266,2807)(267,2806)(268,2805)(269,2804)(270,2803)(271,2802)(272,2801)(273,2800)(274,2799)(275,2798)(276,2797)(277,2796)(278,2795)(279,2794)(280,2793)(281,2792)(282,2791)(283,2790)(284,2789)(285,2788)(286,2787)(287,2786)(288,2785)(289,2784)(290,2783)(291,2782)(292,2781)(293,2780)(294,2779)(295,2778)(296,2777)(297,2776)(298,2775)(299,2774)(300,2773)(301,2772)(302,2771)(303,2770)(304,2769)(305,2768)(306,2767)(307,2766)(308,2765)(309,2764)(310,2763)(311,2762)(312,2761)(313,2760)(314,2759)(315,2758)(316,2757)(317,2756)(318,2755)(319,2754)(320,2753)(321,2752)(322,2751)(323,2750)(324,2749)(325,2748)(326,2747)(327,2746)(328,2745)(329,2744)(330,2743)(331,2742)(332,2741)(333,2740)(334,2739)(335,2738)(336,2737)(337,2736)(338,2735)(339,2734)(340,2733)(341,2732)(342,2731)(343,2730)(344,2729)(345,2728)(346,2727)(347,2726)(348,2725)(349,2724)(350,2723)(351,2722)(352,2721)(353,2720)(354,2719)(355,2718)(356,2717)(357,2716)(358,2715)(359,2714)(360,2713)(361,2712)(362,2711)(363,2710)(364,2709)(365,2708)(366,2707)(367,2706)(368,2705)(369,2704)(370,2703)(371,2702)(372,2701)(373,2700)(374,2699)(375,2698)(376,2697)(377,2696)(378,2695)(379,2694)(380,2693)(381,2692)(382,2691)(383,2690)(384,2689)(385,2688)(386,2687)(387,2686)(388,2685)(389,2684)(390,2683)(391,2682)(392,2681)(393,2680)(394,2679)(395,2678)(396,2677)(397,2676)(398,2675)(399,2674)(400,2673)(401,2672)(402,2671)(403,2670)(404,2669)(405,2668)(406,2667)(407,2666)(408,2665)(409,2664)(410,2663)(411,2662)(412,2661)(413,2660)(414,2659)(415,2658)(416,2657)(417,2656)(418,2655)(419,2654)(420,2653)(421,2652)(422,2651)(423,2650)(424,2649)(425,2648)(426,2647)(427,2646)(428,2645)(429,2644)(430,2643)(431,2642)(432,2641)(433,2640)(434,2639)(435,2638)(436,2637)(437,2636)(438,2635)(439,2634)(440,2633)(441,2632)(442,2631)(443,2630)(444,2629)(445,2628)(446,2627)(447,2626)(448,2625)(449,2624)(450,2623)(451,2622)(452,2621)(453,2620)(454,2619)(455,2618)(456,2617)(457,2616)(458,2615)(459,2614)(460,2613)(461,2612)(462,2611)(463,2610)(464,2609)(465,2608)(466,2607)(467,2606)(468,2605)(469,2604)(470,2603)(471,2602)(472,2601)(473,2600)(474,2599)(475,2598)(476,2597)(477,2596)(478,2595)(479,2594)(480,2593)(481,2592)(482,2591)(483,2590)(484,2589)(485,2588)(486,2587)(487,2586)(488,2585)(489,2584)(490,2583)(491,2582)(492,2581)(493,2580)(494,2579)(495,2578)(496,2577)(497,2576)(498,2575)(499,2574)(500,2573)(501,2572)(502,2571)(503,2570)(504,2569)(505,2568)(506,2567)(507,2566)(508,2565)(509,2564)(510,2563)(511,2562)(512,2561)(513,2560)(514,2559)(515,2558)(516,2557)(517,2556)(518,2555)(519,2554)(520,2553)(521,2552)(522,2551)(523,2550)(524,2549)(525,2548)(526,2547)(527,2546)(528,2545)(529,2544)(530,2543)(531,2542)(532,2541)(533,2540)(534,2539)(535,2538)(536,2537)(537,2536)(538,2535)(539,2534)(540,2533)(541,2532)(542,2531)(543,2530)(544,2529)(545,2528)(546,2527)(547,2526)(548,2525)(549,2524)(550,2523)(551,2522)(552,2521)(553,2520)(554,2519)(555,2518)(556,2517)(557,2516)(558,2515)(559,2514)(560,2513)(561,2512)(562,2511)(563,2510)(564,2509)(565,2508)(566,2507)(567,2506)(568,2505)(569,2504)(570,2503)(571,2502)(572,2501)(573,2500)(574,2499)(575,2498)(576,2497)(577,2496)(578,2495)(579,2494)(580,2493)(581,2492)(582,2491)(583,2490)(584,2489)(585,2488)(586,2487)(587,2486)(588,2485)(589,2484)(590,2483)(591,2482)(592,2481)(593,2480)(594,2479)(595,2478)(596,2477)(597,2476)(598,2475)(599,2474)(600,2473)(601,2472)(602,2471)(603,2470)(604,2469)(605,2468)(606,2467)(607,2466)(608,2465)(609,2464)(610,2463)(611,2462)(612,2461)(613,2460)(614,2459)(615,2458)(616,2457)(617,2456)(618,2455)(619,2454)(620,2453)(621,2452)(622,2451)(623,2450)(624,2449)(625,2448)(626,2447)(627,2446)(628,2445)(629,2444)(630,2443)(631,2442)(632,2441)(633,2440)(634,2439)(635,2438)(636,2437)(637,2436)(638,2435)(639,2434)(640,2433)(641,2432)(642,2431)(643,2430)(644,2429)(645,2428)(646,2427)(647,2426)(648,2425)(649,2424)(650,2423)(651,2422)(652,2421)(653,2420)(654,2419)(655,2418)(656,2417)(657,2416)(658,2415)(659,2414)(660,2413)(661,2412)(662,2411)(663,2410)(664,2409)(665,2408)(666,2407)(667,2406)(668,2405)(669,2404)(670,2403)(671,2402)(672,2401)(673,2400)(674,2399)(675,2398)(676,2397)(677,2396)(678,2395)(679,2394)(680,2393)(681,2392)(682,2391)(683,2390)(684,2389)(685,2388)(686,2387)(687,2386)(688,2385)(689,2384)(690,2383)(691,2382)(692,2381)(693,2380)(694,2379)(695,2378)(696,2377)(697,2376)(698,2375)(699,2374)(700,2373)(701,2372)(702,2371)(703,2370)(704,2369)(705,2368)(706,2367)(707,2366)(708,2365)(709,2364)(710,2363)(711,2362)(712,2361)(713,2360)(714,2359)(715,2358)(716,2357)(717,2356)(718,2355)(719,2354)(720,2353)(721,2352)(722,2351)(723,2350)(724,2349)(725,2348)(726,2347)(727,2346)(728,2345)(729,2344)(730,2343)(731,2342)(732,2341)(733,2340)(734,2339)(735,2338)(736,2337)(737,2336)(738,2335)(739,2334)(740,2333)(741,2332)(742,2331)(743,2330)(744,2329)(745,2328)(746,2327)(747,2326)(748,2325)(749,2324)(750,2323)(751,2322)(752,2321)(753,2320)(754,2319)(755,2318)(756,2317)(757,2316)(758,2315)(759,2314)(760,2313)(761,2312)(762,2311)(763,2310)(764,2309)(765,2308)(766,2307)(767,2306)(768,2305)(769,2304)(770,2303)(771,2302)(772,2301)(773,2300)(774,2299)(775,2298)(776,2297)(777,2296)(778,2295)(779,2294)(780,2293)(781,2292)(782,2291)(783,2290)(784,2289)(785,2288)(786,2287)(787,2286)(788,2285)(789,2284)(790,2283)(791,2282)(792,2281)(793,2280)(794,2279)(795,2278)(796,2277)(797,2276)(798,2275)(799,2274)(800,2273)(801,2272)(802,2271)(803,2270)(804,2269)(805,2268)(806,2267)(807,2266)(808,2265)(809,2264)(810,2263)(811,2262)(812,2261)(813,2260)(814,2259)(815,2258)(816,2257)(817,2256)(818,2255)(819,2254)(820,2253)(821,2252)(822,2251)(823,2250)(824,2249)(825,2248)(826,2247)(827,2246)(828,2245)(829,2244)(830,2243)(831,2242)(832,2241)(833,2240)(834,2239)(835,2238)(836,2237)(837,2236)(838,2235)(839,2234)(840,2233)(841,2232)(842,2231)(843,2230)(844,2229)(845,2228)(846,2227)(847,2226)(848,2225)(849,2224)(850,2223)(851,2222)(852,2221)(853,2220)(854,2219)(855,2218)(856,2217)(857,2216)(858,2215)(859,2214)(860,2213)(861,2212)(862,2211)(863,2210)(864,2209)(865,2208)(866,2207)(867,2206)(868,2205)(869,2204)(870,2203)(871,2202)(872,2201)(873,2200)(874,2199)(875,2198)(876,2197)(877,2196)(878,2195)(879,2194)(880,2193)(881,2192)(882,2191)(883,2190)(884,2189)(885,2188)(886,2187)(887,2186)(888,2185)(889,2184)(890,2183)(891,2182)(892,2181)(893,2180)(894,2179)(895,2178)(896,2177)(897,2176)(898,2175)(899,2174)(900,2173)(901,2172)(902,2171)(903,2170)(904,2169)(905,2168)(906,2167)(907,2166)(908,2165)(909,2164)(910,2163)(911,2162)(912,2161)(913,2160)(914,2159)(915,2158)(916,2157)(917,2156)(918,2155)(919,2154)(920,2153)(921,2152)(922,2151)(923,2150)(924,2149)(925,2148)(926,2147)(927,2146)(928,2145)(929,2144)(930,2143)(931,2142)(932,2141)(933,2140)(934,2139)(935,2138)(936,2137)(937,2136)(938,2135)(939,2134)(940,2133)(941,2132)(942,2131)(943,2130)(944,2129)(945,2128)(946,2127)(947,2126)(948,2125)(949,2124)(950,2123)(951,2122)(952,2121)(953,2120)(954,2119)(955,2118)(956,2117)(957,2116)(958,2115)(959,2114)(960,2113)(961,2112)(962,2111)(963,2110)(964,2109)(965,2108)(966,2107)(967,2106)(968,2105)(969,2104)(970,2103)(971,2102)(972,2101)(973,2100)(974,2099)(975,2098)(976,2097)(977,2096)(978,2095)(979,2094)(980,2093)(981,2092)(982,2091)(983,2090)(984,2089)(985,2088)(986,2087)(987,2086)(988,2085)(989,2084)(990,2083)(991,2082)(992,2081)(993,2080)(994,2079)(995,2078)(996,2077)(997,2076)(998,2075)(999,2074)(1000,2073)(1001,2072)(1002,2071)(1003,2070)(1004,2069)(1005,2068)(1006,2067)(1007,2066)(1008,2065)(1009,2064)(1010,2063)(1011,2062)(1012,2061)(1013,2060)(1014,2059)(1015,2058)(1016,2057)(1017,2056)(1018,2055)(1019,2054)(1020,2053)(1021,2052)(1022,2051)(1023,2050)(1024,2049)(1025,2048)(1026,2047)(1027,2046)(1028,2045)(1029,2044)(1030,2043)(1031,2042)(1032,2041)(1033,2040)(1034,2039)(1035,2038)(1036,2037)(1037,2036)(1038,2035)(1039,2034)(1040,2033)(1041,2032)(1042,2031)(1043,2030)(1044,2029)(1045,2028)(1046,2027)(1047,2026)(1048,2025)(1049,2024)(1050,2023)(1051,2022)(1052,2021)(1053,2020)(1054,2019)(1055,2018)(1056,2017)(1057,2016)(1058,2015)(1059,2014)(1060,2013)(1061,2012)(1062,2011)(1063,2010)(1064,2009)(1065,2008)(1066,2007)(1067,2006)(1068,2005)(1069,2004)(1070,2003)(1071,2002)(1072,2001)(1073,2000)(1074,1999)(1075,1998)(1076,1997)(1077,1996)(1078,1995)(1079,1994)(1080,1993)(1081,1992)(1082,1991)(1083,1990)(1084,1989)(1085,1988)(1086,1987)(1087,1986)(1088,1985)(1089,1984)(1090,1983)(1091,1982)(1092,1981)(1093,1980)(1094,1979)(1095,1978)(1096,1977)(1097,1976)(1098,1975)(1099,1974)(1100,1973)(1101,1972)(1102,1971)(1103,1970)(1104,1969)(1105,1968)(1106,1967)(1107,1966)(1108,1965)(1109,1964)(1110,1963)(1111,1962)(1112,1961)(1113,1960)(1114,1959)(1115,1958)(1116,1957)(1117,1956)(1118,1955)(1119,1954)(1120,1953)(1121,1952)(1122,1951)(1123,1950)(1124,1949)(1125,1948)(1126,1947)(1127,1946)(1128,1945)(1129,1944)(1130,1943)(1131,1942)(1132,1941)(1133,1940)(1134,1939)(1135,1938)(1136,1937)(1137,1936)(1138,1935)(1139,1934)(1140,1933)(1141,1932)(1142,1931)(1143,1930)(1144,1929)(1145,1928)(1146,1927)(1147,1926)(1148,1925)(1149,1924)(1150,1923)(1151,1922)(1152,1921)(1153,1920)(1154,1919)(1155,1918)(1156,1917)(1157,1916)(1158,1915)(1159,1914)(1160,1913)(1161,1912)(1162,1911)(1163,1910)(1164,1909)(1165,1908)(1166,1907)(1167,1906)(1168,1905)(1169,1904)(1170,1903)(1171,1902)(1172,1901)(1173,1900)(1174,1899)(1175,1898)(1176,1897)(1177,1896)(1178,1895)(1179,1894)(1180,1893)(1181,1892)(1182,1891)(1183,1890)(1184,1889)(1185,1888)(1186,1887)(1187,1886)(1188,1885)(1189,1884)(1190,1883)(1191,1882)(1192,1881)(1193,1880)(1194,1879)(1195,1878)(1196,1877)(1197,1876)(1198,1875)(1199,1874)(1200,1873)(1201,1872)(1202,1871)(1203,1870)(1204,1869)(1205,1868)(1206,1867)(1207,1866)(1208,1865)(1209,1864)(1210,1863)(1211,1862)(1212,1861)(1213,1860)(1214,1859)(1215,1858)(1216,1857)(1217,1856)(1218,1855)(1219,1854)(1220,1853)(1221,1852)(1222,1851)(1223,1850)(1224,1849)(1225,1848)(1226,1847)(1227,1846)(1228,1845)(1229,1844)(1230,1843)(1231,1842)(1232,1841)(1233,1840)(1234,1839)(1235,1838)(1236,1837)(1237,1836)(1238,1835)(1239,1834)(1240,1833)(1241,1832)(1242,1831)(1243,1830)(1244,1829)(1245,1828)(1246,1827)(1247,1826)(1248,1825)(1249,1824)(1250,1823)(1251,1822)(1252,1821)(1253,1820)(1254,1819)(1255,1818)(1256,1817)(1257,1816)(1258,1815)(1259,1814)(1260,1813)(1261,1812)(1262,1811)(1263,1810)(1264,1809)(1265,1808)(1266,1807)(1267,1806)(1268,1805)(1269,1804)(1270,1803)(1271,1802)(1272,1801)(1273,1800)(1274,1799)(1275,1798)(1276,1797)(1277,1796)(1278,1795)(1279,1794)(1280,1793)(1281,1792)(1282,1791)(1283,1790)(1284,1789)(1285,1788)(1286,1787)(1287,1786)(1288,1785)(1289,1784)(1290,1783)(1291,1782)(1292,1781)(1293,1780)(1294,1779)(1295,1778)(1296,1777)(1297,1776)(1298,1775)(1299,1774)(1300,1773)(1301,1772)(1302,1771)(1303,1770)(1304,1769)(1305,1768)(1306,1767)(1307,1766)(1308,1765)(1309,1764)(1310,1763)(1311,1762)(1312,1761)(1313,1760)(1314,1759)(1315,1758)(1316,1757)(1317,1756)(1318,1755)(1319,1754)(1320,1753)(1321,1752)(1322,1751)(1323,1750)(1324,1749)(1325,1748)(1326,1747)(1327,1746)(1328,1745)(1329,1744)(1330,1743)(1331,1742)(1332,1741)(1333,1740)(1334,1739)(1335,1738)(1336,1737)(1337,1736)(1338,1735)(1339,1734)(1340,1733)(1341,1732)(1342,1731)(1343,1730)(1344,1729)(1345,1728)(1346,1727)(1347,1726)(1348,1725)(1349,1724)(1350,1723)(1351,1722)(1352,1721)(1353,1720)(1354,1719)(1355,1718)(1356,1717)(1357,1716)(1358,1715)(1359,1714)(1360,1713)(1361,1712)(1362,1711)(1363,1710)(1364,1709)(1365,1708)(1366,1707)(1367,1706)(1368,1705)(1369,1704)(1370,1703)(1371,1702)(1372,1701)(1373,1700)(1374,1699)(1375,1698)(1376,1697)(1377,1696)(1378,1695)(1379,1694)(1380,1693)(1381,1692)(1382,1691)(1383,1690)(1384,1689)(1385,1688)(1386,1687)(1387,1686)(1388,1685)(1389,1684)(1390,1683)(1391,1682)(1392,1681)(1393,1680)(1394,1679)(1395,1678)(1396,1677)(1397,1676)(1398,1675)(1399,1674)(1400,1673)(1401,1672)(1402,1671)(1403,1670)(1404,1669)(1405,1668)(1406,1667)(1407,1666)(1408,1665)(1409,1664)(1410,1663)(1411,1662)(1412,1661)(1413,1660)(1414,1659)(1415,1658)(1416,1657)(1417,1656)(1418,1655)(1419,1654)(1420,1653)(1421,1652)(1422,1651)(1423,1650)(1424,1649)(1425,1648)(1426,1647)(1427,1646)(1428,1645)(1429,1644)(1430,1643)(1431,1642)(1432,1641)(1433,1640)(1434,1639)(1435,1638)(1436,1637)(1437,1636)(1438,1635)(1439,1634)(1440,1633)(1441,1632)(1442,1631)(1443,1630)(1444,1629)(1445,1628)(1446,1627)(1447,1626)(1448,1625)(1449,1624)(1450,1623)(1451,1622)(1452,1621)(1453,1620)(1454,1619)(1455,1618)(1456,1617)(1457,1616)(1458,1615)(1459,1614)(1460,1613)(1461,1612)(1462,1611)(1463,1610)(1464,1609)(1465,1608)(1466,1607)(1467,1606)(1468,1605)(1469,1604)(1470,1603)(1471,1602)(1472,1601)(1473,1600)(1474,1599)(1475,1598)(1476,1597)(1477,1596)(1478,1595)(1479,1594)(1480,1593)(1481,1592)(1482,1591)(1483,1590)(1484,1589)(1485,1588)(1486,1587)(1487,1586)(1488,1585)(1489,1584)(1490,1583)(1491,1582)(1492,1581)(1493,1580)(1494,1579)(1495,1578)(1496,1577)(1497,1576)(1498,1575)(1499,1574)(1500,1573)(1501,1572)(1502,1571)(1503,1570)(1504,1569)(1505,1568)(1506,1567)(1507,1566)(1508,1565)(1509,1564)(1510,1563)(1511,1562)(1512,1561)(1513,1560)(1514,1559)(1515,1558)(1516,1557)(1517,1556)(1518,1555)(1519,1554)(1520,1553)(1521,1552)(1522,1551)(1523,1550)(1524,1549)(1525,1548)(1526,1547)(1527,1546)(1528,1545)(1529,1544)(1530,1543)(1531,1542)(1532,1541)(1533,1540)(1534,1539)(1535,1538)(1536,1537)
Polycyclic presentation:
2,5,3061|b^a=b^4,c^a=c^3060
Conjugacy classes & character table
7654 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30610, 5);
Finite Group Databasebeta