← Prev (#44477319) Next (#44477321) →
D15205 #44477320
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3046 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);(2,5)(3,4)(7,3046)(8,3045)(9,3044)(10,3043)(11,3042)(12,3041)(13,3040)(14,3039)(15,3038)(16,3037)(17,3036)(18,3035)(19,3034)(20,3033)(21,3032)(22,3031)(23,3030)(24,3029)(25,3028)(26,3027)(27,3026)(28,3025)(29,3024)(30,3023)(31,3022)(32,3021)(33,3020)(34,3019)(35,3018)(36,3017)(37,3016)(38,3015)(39,3014)(40,3013)(41,3012)(42,3011)(43,3010)(44,3009)(45,3008)(46,3007)(47,3006)(48,3005)(49,3004)(50,3003)(51,3002)(52,3001)(53,3000)(54,2999)(55,2998)(56,2997)(57,2996)(58,2995)(59,2994)(60,2993)(61,2992)(62,2991)(63,2990)(64,2989)(65,2988)(66,2987)(67,2986)(68,2985)(69,2984)(70,2983)(71,2982)(72,2981)(73,2980)(74,2979)(75,2978)(76,2977)(77,2976)(78,2975)(79,2974)(80,2973)(81,2972)(82,2971)(83,2970)(84,2969)(85,2968)(86,2967)(87,2966)(88,2965)(89,2964)(90,2963)(91,2962)(92,2961)(93,2960)(94,2959)(95,2958)(96,2957)(97,2956)(98,2955)(99,2954)(100,2953)(101,2952)(102,2951)(103,2950)(104,2949)(105,2948)(106,2947)(107,2946)(108,2945)(109,2944)(110,2943)(111,2942)(112,2941)(113,2940)(114,2939)(115,2938)(116,2937)(117,2936)(118,2935)(119,2934)(120,2933)(121,2932)(122,2931)(123,2930)(124,2929)(125,2928)(126,2927)(127,2926)(128,2925)(129,2924)(130,2923)(131,2922)(132,2921)(133,2920)(134,2919)(135,2918)(136,2917)(137,2916)(138,2915)(139,2914)(140,2913)(141,2912)(142,2911)(143,2910)(144,2909)(145,2908)(146,2907)(147,2906)(148,2905)(149,2904)(150,2903)(151,2902)(152,2901)(153,2900)(154,2899)(155,2898)(156,2897)(157,2896)(158,2895)(159,2894)(160,2893)(161,2892)(162,2891)(163,2890)(164,2889)(165,2888)(166,2887)(167,2886)(168,2885)(169,2884)(170,2883)(171,2882)(172,2881)(173,2880)(174,2879)(175,2878)(176,2877)(177,2876)(178,2875)(179,2874)(180,2873)(181,2872)(182,2871)(183,2870)(184,2869)(185,2868)(186,2867)(187,2866)(188,2865)(189,2864)(190,2863)(191,2862)(192,2861)(193,2860)(194,2859)(195,2858)(196,2857)(197,2856)(198,2855)(199,2854)(200,2853)(201,2852)(202,2851)(203,2850)(204,2849)(205,2848)(206,2847)(207,2846)(208,2845)(209,2844)(210,2843)(211,2842)(212,2841)(213,2840)(214,2839)(215,2838)(216,2837)(217,2836)(218,2835)(219,2834)(220,2833)(221,2832)(222,2831)(223,2830)(224,2829)(225,2828)(226,2827)(227,2826)(228,2825)(229,2824)(230,2823)(231,2822)(232,2821)(233,2820)(234,2819)(235,2818)(236,2817)(237,2816)(238,2815)(239,2814)(240,2813)(241,2812)(242,2811)(243,2810)(244,2809)(245,2808)(246,2807)(247,2806)(248,2805)(249,2804)(250,2803)(251,2802)(252,2801)(253,2800)(254,2799)(255,2798)(256,2797)(257,2796)(258,2795)(259,2794)(260,2793)(261,2792)(262,2791)(263,2790)(264,2789)(265,2788)(266,2787)(267,2786)(268,2785)(269,2784)(270,2783)(271,2782)(272,2781)(273,2780)(274,2779)(275,2778)(276,2777)(277,2776)(278,2775)(279,2774)(280,2773)(281,2772)(282,2771)(283,2770)(284,2769)(285,2768)(286,2767)(287,2766)(288,2765)(289,2764)(290,2763)(291,2762)(292,2761)(293,2760)(294,2759)(295,2758)(296,2757)(297,2756)(298,2755)(299,2754)(300,2753)(301,2752)(302,2751)(303,2750)(304,2749)(305,2748)(306,2747)(307,2746)(308,2745)(309,2744)(310,2743)(311,2742)(312,2741)(313,2740)(314,2739)(315,2738)(316,2737)(317,2736)(318,2735)(319,2734)(320,2733)(321,2732)(322,2731)(323,2730)(324,2729)(325,2728)(326,2727)(327,2726)(328,2725)(329,2724)(330,2723)(331,2722)(332,2721)(333,2720)(334,2719)(335,2718)(336,2717)(337,2716)(338,2715)(339,2714)(340,2713)(341,2712)(342,2711)(343,2710)(344,2709)(345,2708)(346,2707)(347,2706)(348,2705)(349,2704)(350,2703)(351,2702)(352,2701)(353,2700)(354,2699)(355,2698)(356,2697)(357,2696)(358,2695)(359,2694)(360,2693)(361,2692)(362,2691)(363,2690)(364,2689)(365,2688)(366,2687)(367,2686)(368,2685)(369,2684)(370,2683)(371,2682)(372,2681)(373,2680)(374,2679)(375,2678)(376,2677)(377,2676)(378,2675)(379,2674)(380,2673)(381,2672)(382,2671)(383,2670)(384,2669)(385,2668)(386,2667)(387,2666)(388,2665)(389,2664)(390,2663)(391,2662)(392,2661)(393,2660)(394,2659)(395,2658)(396,2657)(397,2656)(398,2655)(399,2654)(400,2653)(401,2652)(402,2651)(403,2650)(404,2649)(405,2648)(406,2647)(407,2646)(408,2645)(409,2644)(410,2643)(411,2642)(412,2641)(413,2640)(414,2639)(415,2638)(416,2637)(417,2636)(418,2635)(419,2634)(420,2633)(421,2632)(422,2631)(423,2630)(424,2629)(425,2628)(426,2627)(427,2626)(428,2625)(429,2624)(430,2623)(431,2622)(432,2621)(433,2620)(434,2619)(435,2618)(436,2617)(437,2616)(438,2615)(439,2614)(440,2613)(441,2612)(442,2611)(443,2610)(444,2609)(445,2608)(446,2607)(447,2606)(448,2605)(449,2604)(450,2603)(451,2602)(452,2601)(453,2600)(454,2599)(455,2598)(456,2597)(457,2596)(458,2595)(459,2594)(460,2593)(461,2592)(462,2591)(463,2590)(464,2589)(465,2588)(466,2587)(467,2586)(468,2585)(469,2584)(470,2583)(471,2582)(472,2581)(473,2580)(474,2579)(475,2578)(476,2577)(477,2576)(478,2575)(479,2574)(480,2573)(481,2572)(482,2571)(483,2570)(484,2569)(485,2568)(486,2567)(487,2566)(488,2565)(489,2564)(490,2563)(491,2562)(492,2561)(493,2560)(494,2559)(495,2558)(496,2557)(497,2556)(498,2555)(499,2554)(500,2553)(501,2552)(502,2551)(503,2550)(504,2549)(505,2548)(506,2547)(507,2546)(508,2545)(509,2544)(510,2543)(511,2542)(512,2541)(513,2540)(514,2539)(515,2538)(516,2537)(517,2536)(518,2535)(519,2534)(520,2533)(521,2532)(522,2531)(523,2530)(524,2529)(525,2528)(526,2527)(527,2526)(528,2525)(529,2524)(530,2523)(531,2522)(532,2521)(533,2520)(534,2519)(535,2518)(536,2517)(537,2516)(538,2515)(539,2514)(540,2513)(541,2512)(542,2511)(543,2510)(544,2509)(545,2508)(546,2507)(547,2506)(548,2505)(549,2504)(550,2503)(551,2502)(552,2501)(553,2500)(554,2499)(555,2498)(556,2497)(557,2496)(558,2495)(559,2494)(560,2493)(561,2492)(562,2491)(563,2490)(564,2489)(565,2488)(566,2487)(567,2486)(568,2485)(569,2484)(570,2483)(571,2482)(572,2481)(573,2480)(574,2479)(575,2478)(576,2477)(577,2476)(578,2475)(579,2474)(580,2473)(581,2472)(582,2471)(583,2470)(584,2469)(585,2468)(586,2467)(587,2466)(588,2465)(589,2464)(590,2463)(591,2462)(592,2461)(593,2460)(594,2459)(595,2458)(596,2457)(597,2456)(598,2455)(599,2454)(600,2453)(601,2452)(602,2451)(603,2450)(604,2449)(605,2448)(606,2447)(607,2446)(608,2445)(609,2444)(610,2443)(611,2442)(612,2441)(613,2440)(614,2439)(615,2438)(616,2437)(617,2436)(618,2435)(619,2434)(620,2433)(621,2432)(622,2431)(623,2430)(624,2429)(625,2428)(626,2427)(627,2426)(628,2425)(629,2424)(630,2423)(631,2422)(632,2421)(633,2420)(634,2419)(635,2418)(636,2417)(637,2416)(638,2415)(639,2414)(640,2413)(641,2412)(642,2411)(643,2410)(644,2409)(645,2408)(646,2407)(647,2406)(648,2405)(649,2404)(650,2403)(651,2402)(652,2401)(653,2400)(654,2399)(655,2398)(656,2397)(657,2396)(658,2395)(659,2394)(660,2393)(661,2392)(662,2391)(663,2390)(664,2389)(665,2388)(666,2387)(667,2386)(668,2385)(669,2384)(670,2383)(671,2382)(672,2381)(673,2380)(674,2379)(675,2378)(676,2377)(677,2376)(678,2375)(679,2374)(680,2373)(681,2372)(682,2371)(683,2370)(684,2369)(685,2368)(686,2367)(687,2366)(688,2365)(689,2364)(690,2363)(691,2362)(692,2361)(693,2360)(694,2359)(695,2358)(696,2357)(697,2356)(698,2355)(699,2354)(700,2353)(701,2352)(702,2351)(703,2350)(704,2349)(705,2348)(706,2347)(707,2346)(708,2345)(709,2344)(710,2343)(711,2342)(712,2341)(713,2340)(714,2339)(715,2338)(716,2337)(717,2336)(718,2335)(719,2334)(720,2333)(721,2332)(722,2331)(723,2330)(724,2329)(725,2328)(726,2327)(727,2326)(728,2325)(729,2324)(730,2323)(731,2322)(732,2321)(733,2320)(734,2319)(735,2318)(736,2317)(737,2316)(738,2315)(739,2314)(740,2313)(741,2312)(742,2311)(743,2310)(744,2309)(745,2308)(746,2307)(747,2306)(748,2305)(749,2304)(750,2303)(751,2302)(752,2301)(753,2300)(754,2299)(755,2298)(756,2297)(757,2296)(758,2295)(759,2294)(760,2293)(761,2292)(762,2291)(763,2290)(764,2289)(765,2288)(766,2287)(767,2286)(768,2285)(769,2284)(770,2283)(771,2282)(772,2281)(773,2280)(774,2279)(775,2278)(776,2277)(777,2276)(778,2275)(779,2274)(780,2273)(781,2272)(782,2271)(783,2270)(784,2269)(785,2268)(786,2267)(787,2266)(788,2265)(789,2264)(790,2263)(791,2262)(792,2261)(793,2260)(794,2259)(795,2258)(796,2257)(797,2256)(798,2255)(799,2254)(800,2253)(801,2252)(802,2251)(803,2250)(804,2249)(805,2248)(806,2247)(807,2246)(808,2245)(809,2244)(810,2243)(811,2242)(812,2241)(813,2240)(814,2239)(815,2238)(816,2237)(817,2236)(818,2235)(819,2234)(820,2233)(821,2232)(822,2231)(823,2230)(824,2229)(825,2228)(826,2227)(827,2226)(828,2225)(829,2224)(830,2223)(831,2222)(832,2221)(833,2220)(834,2219)(835,2218)(836,2217)(837,2216)(838,2215)(839,2214)(840,2213)(841,2212)(842,2211)(843,2210)(844,2209)(845,2208)(846,2207)(847,2206)(848,2205)(849,2204)(850,2203)(851,2202)(852,2201)(853,2200)(854,2199)(855,2198)(856,2197)(857,2196)(858,2195)(859,2194)(860,2193)(861,2192)(862,2191)(863,2190)(864,2189)(865,2188)(866,2187)(867,2186)(868,2185)(869,2184)(870,2183)(871,2182)(872,2181)(873,2180)(874,2179)(875,2178)(876,2177)(877,2176)(878,2175)(879,2174)(880,2173)(881,2172)(882,2171)(883,2170)(884,2169)(885,2168)(886,2167)(887,2166)(888,2165)(889,2164)(890,2163)(891,2162)(892,2161)(893,2160)(894,2159)(895,2158)(896,2157)(897,2156)(898,2155)(899,2154)(900,2153)(901,2152)(902,2151)(903,2150)(904,2149)(905,2148)(906,2147)(907,2146)(908,2145)(909,2144)(910,2143)(911,2142)(912,2141)(913,2140)(914,2139)(915,2138)(916,2137)(917,2136)(918,2135)(919,2134)(920,2133)(921,2132)(922,2131)(923,2130)(924,2129)(925,2128)(926,2127)(927,2126)(928,2125)(929,2124)(930,2123)(931,2122)(932,2121)(933,2120)(934,2119)(935,2118)(936,2117)(937,2116)(938,2115)(939,2114)(940,2113)(941,2112)(942,2111)(943,2110)(944,2109)(945,2108)(946,2107)(947,2106)(948,2105)(949,2104)(950,2103)(951,2102)(952,2101)(953,2100)(954,2099)(955,2098)(956,2097)(957,2096)(958,2095)(959,2094)(960,2093)(961,2092)(962,2091)(963,2090)(964,2089)(965,2088)(966,2087)(967,2086)(968,2085)(969,2084)(970,2083)(971,2082)(972,2081)(973,2080)(974,2079)(975,2078)(976,2077)(977,2076)(978,2075)(979,2074)(980,2073)(981,2072)(982,2071)(983,2070)(984,2069)(985,2068)(986,2067)(987,2066)(988,2065)(989,2064)(990,2063)(991,2062)(992,2061)(993,2060)(994,2059)(995,2058)(996,2057)(997,2056)(998,2055)(999,2054)(1000,2053)(1001,2052)(1002,2051)(1003,2050)(1004,2049)(1005,2048)(1006,2047)(1007,2046)(1008,2045)(1009,2044)(1010,2043)(1011,2042)(1012,2041)(1013,2040)(1014,2039)(1015,2038)(1016,2037)(1017,2036)(1018,2035)(1019,2034)(1020,2033)(1021,2032)(1022,2031)(1023,2030)(1024,2029)(1025,2028)(1026,2027)(1027,2026)(1028,2025)(1029,2024)(1030,2023)(1031,2022)(1032,2021)(1033,2020)(1034,2019)(1035,2018)(1036,2017)(1037,2016)(1038,2015)(1039,2014)(1040,2013)(1041,2012)(1042,2011)(1043,2010)(1044,2009)(1045,2008)(1046,2007)(1047,2006)(1048,2005)(1049,2004)(1050,2003)(1051,2002)(1052,2001)(1053,2000)(1054,1999)(1055,1998)(1056,1997)(1057,1996)(1058,1995)(1059,1994)(1060,1993)(1061,1992)(1062,1991)(1063,1990)(1064,1989)(1065,1988)(1066,1987)(1067,1986)(1068,1985)(1069,1984)(1070,1983)(1071,1982)(1072,1981)(1073,1980)(1074,1979)(1075,1978)(1076,1977)(1077,1976)(1078,1975)(1079,1974)(1080,1973)(1081,1972)(1082,1971)(1083,1970)(1084,1969)(1085,1968)(1086,1967)(1087,1966)(1088,1965)(1089,1964)(1090,1963)(1091,1962)(1092,1961)(1093,1960)(1094,1959)(1095,1958)(1096,1957)(1097,1956)(1098,1955)(1099,1954)(1100,1953)(1101,1952)(1102,1951)(1103,1950)(1104,1949)(1105,1948)(1106,1947)(1107,1946)(1108,1945)(1109,1944)(1110,1943)(1111,1942)(1112,1941)(1113,1940)(1114,1939)(1115,1938)(1116,1937)(1117,1936)(1118,1935)(1119,1934)(1120,1933)(1121,1932)(1122,1931)(1123,1930)(1124,1929)(1125,1928)(1126,1927)(1127,1926)(1128,1925)(1129,1924)(1130,1923)(1131,1922)(1132,1921)(1133,1920)(1134,1919)(1135,1918)(1136,1917)(1137,1916)(1138,1915)(1139,1914)(1140,1913)(1141,1912)(1142,1911)(1143,1910)(1144,1909)(1145,1908)(1146,1907)(1147,1906)(1148,1905)(1149,1904)(1150,1903)(1151,1902)(1152,1901)(1153,1900)(1154,1899)(1155,1898)(1156,1897)(1157,1896)(1158,1895)(1159,1894)(1160,1893)(1161,1892)(1162,1891)(1163,1890)(1164,1889)(1165,1888)(1166,1887)(1167,1886)(1168,1885)(1169,1884)(1170,1883)(1171,1882)(1172,1881)(1173,1880)(1174,1879)(1175,1878)(1176,1877)(1177,1876)(1178,1875)(1179,1874)(1180,1873)(1181,1872)(1182,1871)(1183,1870)(1184,1869)(1185,1868)(1186,1867)(1187,1866)(1188,1865)(1189,1864)(1190,1863)(1191,1862)(1192,1861)(1193,1860)(1194,1859)(1195,1858)(1196,1857)(1197,1856)(1198,1855)(1199,1854)(1200,1853)(1201,1852)(1202,1851)(1203,1850)(1204,1849)(1205,1848)(1206,1847)(1207,1846)(1208,1845)(1209,1844)(1210,1843)(1211,1842)(1212,1841)(1213,1840)(1214,1839)(1215,1838)(1216,1837)(1217,1836)(1218,1835)(1219,1834)(1220,1833)(1221,1832)(1222,1831)(1223,1830)(1224,1829)(1225,1828)(1226,1827)(1227,1826)(1228,1825)(1229,1824)(1230,1823)(1231,1822)(1232,1821)(1233,1820)(1234,1819)(1235,1818)(1236,1817)(1237,1816)(1238,1815)(1239,1814)(1240,1813)(1241,1812)(1242,1811)(1243,1810)(1244,1809)(1245,1808)(1246,1807)(1247,1806)(1248,1805)(1249,1804)(1250,1803)(1251,1802)(1252,1801)(1253,1800)(1254,1799)(1255,1798)(1256,1797)(1257,1796)(1258,1795)(1259,1794)(1260,1793)(1261,1792)(1262,1791)(1263,1790)(1264,1789)(1265,1788)(1266,1787)(1267,1786)(1268,1785)(1269,1784)(1270,1783)(1271,1782)(1272,1781)(1273,1780)(1274,1779)(1275,1778)(1276,1777)(1277,1776)(1278,1775)(1279,1774)(1280,1773)(1281,1772)(1282,1771)(1283,1770)(1284,1769)(1285,1768)(1286,1767)(1287,1766)(1288,1765)(1289,1764)(1290,1763)(1291,1762)(1292,1761)(1293,1760)(1294,1759)(1295,1758)(1296,1757)(1297,1756)(1298,1755)(1299,1754)(1300,1753)(1301,1752)(1302,1751)(1303,1750)(1304,1749)(1305,1748)(1306,1747)(1307,1746)(1308,1745)(1309,1744)(1310,1743)(1311,1742)(1312,1741)(1313,1740)(1314,1739)(1315,1738)(1316,1737)(1317,1736)(1318,1735)(1319,1734)(1320,1733)(1321,1732)(1322,1731)(1323,1730)(1324,1729)(1325,1728)(1326,1727)(1327,1726)(1328,1725)(1329,1724)(1330,1723)(1331,1722)(1332,1721)(1333,1720)(1334,1719)(1335,1718)(1336,1717)(1337,1716)(1338,1715)(1339,1714)(1340,1713)(1341,1712)(1342,1711)(1343,1710)(1344,1709)(1345,1708)(1346,1707)(1347,1706)(1348,1705)(1349,1704)(1350,1703)(1351,1702)(1352,1701)(1353,1700)(1354,1699)(1355,1698)(1356,1697)(1357,1696)(1358,1695)(1359,1694)(1360,1693)(1361,1692)(1362,1691)(1363,1690)(1364,1689)(1365,1688)(1366,1687)(1367,1686)(1368,1685)(1369,1684)(1370,1683)(1371,1682)(1372,1681)(1373,1680)(1374,1679)(1375,1678)(1376,1677)(1377,1676)(1378,1675)(1379,1674)(1380,1673)(1381,1672)(1382,1671)(1383,1670)(1384,1669)(1385,1668)(1386,1667)(1387,1666)(1388,1665)(1389,1664)(1390,1663)(1391,1662)(1392,1661)(1393,1660)(1394,1659)(1395,1658)(1396,1657)(1397,1656)(1398,1655)(1399,1654)(1400,1653)(1401,1652)(1402,1651)(1403,1650)(1404,1649)(1405,1648)(1406,1647)(1407,1646)(1408,1645)(1409,1644)(1410,1643)(1411,1642)(1412,1641)(1413,1640)(1414,1639)(1415,1638)(1416,1637)(1417,1636)(1418,1635)(1419,1634)(1420,1633)(1421,1632)(1422,1631)(1423,1630)(1424,1629)(1425,1628)(1426,1627)(1427,1626)(1428,1625)(1429,1624)(1430,1623)(1431,1622)(1432,1621)(1433,1620)(1434,1619)(1435,1618)(1436,1617)(1437,1616)(1438,1615)(1439,1614)(1440,1613)(1441,1612)(1442,1611)(1443,1610)(1444,1609)(1445,1608)(1446,1607)(1447,1606)(1448,1605)(1449,1604)(1450,1603)(1451,1602)(1452,1601)(1453,1600)(1454,1599)(1455,1598)(1456,1597)(1457,1596)(1458,1595)(1459,1594)(1460,1593)(1461,1592)(1462,1591)(1463,1590)(1464,1589)(1465,1588)(1466,1587)(1467,1586)(1468,1585)(1469,1584)(1470,1583)(1471,1582)(1472,1581)(1473,1580)(1474,1579)(1475,1578)(1476,1577)(1477,1576)(1478,1575)(1479,1574)(1480,1573)(1481,1572)(1482,1571)(1483,1570)(1484,1569)(1485,1568)(1486,1567)(1487,1566)(1488,1565)(1489,1564)(1490,1563)(1491,1562)(1492,1561)(1493,1560)(1494,1559)(1495,1558)(1496,1557)(1497,1556)(1498,1555)(1499,1554)(1500,1553)(1501,1552)(1502,1551)(1503,1550)(1504,1549)(1505,1548)(1506,1547)(1507,1546)(1508,1545)(1509,1544)(1510,1543)(1511,1542)(1512,1541)(1513,1540)(1514,1539)(1515,1538)(1516,1537)(1517,1536)(1518,1535)(1519,1534)(1520,1533)(1521,1532)(1522,1531)(1523,1530)(1524,1529)(1525,1528)(1526,1527)
Polycyclic presentation:
2,5,3041|b^a=b^4,c^a=c^3040
Conjugacy classes & character table
7604 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30410, 5);
Finite Group Databasebeta