Finite Group Databasebeta

?

← Prev (#38760840) Next (#38760842) →

D₁₂₆₅₂ #38760841

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 3167 points:

(1,2,3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,2721,2722,2723,2724,2725,2726,2727,2728,2729,2730,2731,2732,2733,2734,2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,2751,2752,2753,2754,2755,2756,2757,2758,2759,2760,2761,2762,2763,2764,2765,2766,2767,2768,2769,2770,2771,2772,2773,2774,2775,2776,2777,2778,2779,2780,2781,2782,2783,2784,2785,2786,2787,2788,2789,2790,2791,2792,2793,2794,2795,2796,2797,2798,2799,2800,2801,2802,2803,2804,2805,2806,2807,2808,2809,2810,2811,2812,2813,2814,2815,2816,2817,2818,2819,2820,2821,2822,2823,2824,2825,2826,2827,2828,2829,2830,2831,2832,2833,2834,2835,2836,2837,2838,2839,2840,2841,2842,2843,2844,2845,2846,2847,2848,2849,2850,2851,2852,2853,2854,2855,2856,2857,2858,2859,2860,2861,2862,2863,2864,2865,2866,2867,2868,2869,2870,2871,2872,2873,2874,2875,2876,2877,2878,2879,2880,2881,2882,2883,2884,2885,2886,2887,2888,2889,2890,2891,2892,2893,2894,2895,2896,2897,2898,2899,2900,2901,2902,2903,2904,2905,2906,2907,2908,2909,2910,2911,2912,2913,2914,2915,2916,2917,2918,2919,2920,2921,2922,2923,2924,2925,2926,2927,2928,2929,2930,2931,2932,2933,2934,2935,2936,2937,2938,2939,2940,2941,2942,2943,2944,2945,2946,2947,2948,2949,2950,2951,2952,2953,2954,2955,2956,2957,2958,2959,2960,2961,2962,2963,2964,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,2977,2978,2979,2980,2981,2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003,3004,3005,3006,3007,3008,3009,3010,3011,3012,3013,3014,3015,3016,3017,3018,3019,3020,3021,3022,3023,3024,3025,3026,3027,3028,3029,3030,3031,3032,3033,3034,3035,3036,3037,3038,3039,3040,3041,3042,3043,3044,3045,3046,3047,3048,3049,3050,3051,3052,3053,3054,3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,3067,3068,3069,3070,3071,3072,3073,3074,3075,3076,3077,3078,3079,3080,3081,3082,3083,3084,3085,3086,3087,3088,3089,3090,3091,3092,3093,3094,3095,3096,3097,3098,3099,3100,3101,3102,3103,3104,3105,3106,3107,3108,3109,3110,3111,3112,3113,3114,3115,3116,3117,3118,3119,3120,3121,3122,3123,3124,3125,3126,3127,3128,3129,3130,3131,3132,3133,3134,3135,3136,3137,3138,3139,3140,3141,3142,3143,3144,3145,3146,3147,3148,3149,3150,3151,3152,3153,3154,3155,3156,3157,3158,3159,3160,3161,3162,3163,3164,3165,3166,3167);(2,4)(6,3167)(7,3166)(8,3165)(9,3164)(10,3163)(11,3162)(12,3161)(13,3160)(14,3159)(15,3158)(16,3157)(17,3156)(18,3155)(19,3154)(20,3153)(21,3152)(22,3151)(23,3150)(24,3149)(25,3148)(26,3147)(27,3146)(28,3145)(29,3144)(30,3143)(31,3142)(32,3141)(33,3140)(34,3139)(35,3138)(36,3137)(37,3136)(38,3135)(39,3134)(40,3133)(41,3132)(42,3131)(43,3130)(44,3129)(45,3128)(46,3127)(47,3126)(48,3125)(49,3124)(50,3123)(51,3122)(52,3121)(53,3120)(54,3119)(55,3118)(56,3117)(57,3116)(58,3115)(59,3114)(60,3113)(61,3112)(62,3111)(63,3110)(64,3109)(65,3108)(66,3107)(67,3106)(68,3105)(69,3104)(70,3103)(71,3102)(72,3101)(73,3100)(74,3099)(75,3098)(76,3097)(77,3096)(78,3095)(79,3094)(80,3093)(81,3092)(82,3091)(83,3090)(84,3089)(85,3088)(86,3087)(87,3086)(88,3085)(89,3084)(90,3083)(91,3082)(92,3081)(93,3080)(94,3079)(95,3078)(96,3077)(97,3076)(98,3075)(99,3074)(100,3073)(101,3072)(102,3071)(103,3070)(104,3069)(105,3068)(106,3067)(107,3066)(108,3065)(109,3064)(110,3063)(111,3062)(112,3061)(113,3060)(114,3059)(115,3058)(116,3057)(117,3056)(118,3055)(119,3054)(120,3053)(121,3052)(122,3051)(123,3050)(124,3049)(125,3048)(126,3047)(127,3046)(128,3045)(129,3044)(130,3043)(131,3042)(132,3041)(133,3040)(134,3039)(135,3038)(136,3037)(137,3036)(138,3035)(139,3034)(140,3033)(141,3032)(142,3031)(143,3030)(144,3029)(145,3028)(146,3027)(147,3026)(148,3025)(149,3024)(150,3023)(151,3022)(152,3021)(153,3020)(154,3019)(155,3018)(156,3017)(157,3016)(158,3015)(159,3014)(160,3013)(161,3012)(162,3011)(163,3010)(164,3009)(165,3008)(166,3007)(167,3006)(168,3005)(169,3004)(170,3003)(171,3002)(172,3001)(173,3000)(174,2999)(175,2998)(176,2997)(177,2996)(178,2995)(179,2994)(180,2993)(181,2992)(182,2991)(183,2990)(184,2989)(185,2988)(186,2987)(187,2986)(188,2985)(189,2984)(190,2983)(191,2982)(192,2981)(193,2980)(194,2979)(195,2978)(196,2977)(197,2976)(198,2975)(199,2974)(200,2973)(201,2972)(202,2971)(203,2970)(204,2969)(205,2968)(206,2967)(207,2966)(208,2965)(209,2964)(210,2963)(211,2962)(212,2961)(213,2960)(214,2959)(215,2958)(216,2957)(217,2956)(218,2955)(219,2954)(220,2953)(221,2952)(222,2951)(223,2950)(224,2949)(225,2948)(226,2947)(227,2946)(228,2945)(229,2944)(230,2943)(231,2942)(232,2941)(233,2940)(234,2939)(235,2938)(236,2937)(237,2936)(238,2935)(239,2934)(240,2933)(241,2932)(242,2931)(243,2930)(244,2929)(245,2928)(246,2927)(247,2926)(248,2925)(249,2924)(250,2923)(251,2922)(252,2921)(253,2920)(254,2919)(255,2918)(256,2917)(257,2916)(258,2915)(259,2914)(260,2913)(261,2912)(262,2911)(263,2910)(264,2909)(265,2908)(266,2907)(267,2906)(268,2905)(269,2904)(270,2903)(271,2902)(272,2901)(273,2900)(274,2899)(275,2898)(276,2897)(277,2896)(278,2895)(279,2894)(280,2893)(281,2892)(282,2891)(283,2890)(284,2889)(285,2888)(286,2887)(287,2886)(288,2885)(289,2884)(290,2883)(291,2882)(292,2881)(293,2880)(294,2879)(295,2878)(296,2877)(297,2876)(298,2875)(299,2874)(300,2873)(301,2872)(302,2871)(303,2870)(304,2869)(305,2868)(306,2867)(307,2866)(308,2865)(309,2864)(310,2863)(311,2862)(312,2861)(313,2860)(314,2859)(315,2858)(316,2857)(317,2856)(318,2855)(319,2854)(320,2853)(321,2852)(322,2851)(323,2850)(324,2849)(325,2848)(326,2847)(327,2846)(328,2845)(329,2844)(330,2843)(331,2842)(332,2841)(333,2840)(334,2839)(335,2838)(336,2837)(337,2836)(338,2835)(339,2834)(340,2833)(341,2832)(342,2831)(343,2830)(344,2829)(345,2828)(346,2827)(347,2826)(348,2825)(349,2824)(350,2823)(351,2822)(352,2821)(353,2820)(354,2819)(355,2818)(356,2817)(357,2816)(358,2815)(359,2814)(360,2813)(361,2812)(362,2811)(363,2810)(364,2809)(365,2808)(366,2807)(367,2806)(368,2805)(369,2804)(370,2803)(371,2802)(372,2801)(373,2800)(374,2799)(375,2798)(376,2797)(377,2796)(378,2795)(379,2794)(380,2793)(381,2792)(382,2791)(383,2790)(384,2789)(385,2788)(386,2787)(387,2786)(388,2785)(389,2784)(390,2783)(391,2782)(392,2781)(393,2780)(394,2779)(395,2778)(396,2777)(397,2776)(398,2775)(399,2774)(400,2773)(401,2772)(402,2771)(403,2770)(404,2769)(405,2768)(406,2767)(407,2766)(408,2765)(409,2764)(410,2763)(411,2762)(412,2761)(413,2760)(414,2759)(415,2758)(416,2757)(417,2756)(418,2755)(419,2754)(420,2753)(421,2752)(422,2751)(423,2750)(424,2749)(425,2748)(426,2747)(427,2746)(428,2745)(429,2744)(430,2743)(431,2742)(432,2741)(433,2740)(434,2739)(435,2738)(436,2737)(437,2736)(438,2735)(439,2734)(440,2733)(441,2732)(442,2731)(443,2730)(444,2729)(445,2728)(446,2727)(447,2726)(448,2725)(449,2724)(450,2723)(451,2722)(452,2721)(453,2720)(454,2719)(455,2718)(456,2717)(457,2716)(458,2715)(459,2714)(460,2713)(461,2712)(462,2711)(463,2710)(464,2709)(465,2708)(466,2707)(467,2706)(468,2705)(469,2704)(470,2703)(471,2702)(472,2701)(473,2700)(474,2699)(475,2698)(476,2697)(477,2696)(478,2695)(479,2694)(480,2693)(481,2692)(482,2691)(483,2690)(484,2689)(485,2688)(486,2687)(487,2686)(488,2685)(489,2684)(490,2683)(491,2682)(492,2681)(493,2680)(494,2679)(495,2678)(496,2677)(497,2676)(498,2675)(499,2674)(500,2673)(501,2672)(502,2671)(503,2670)(504,2669)(505,2668)(506,2667)(507,2666)(508,2665)(509,2664)(510,2663)(511,2662)(512,2661)(513,2660)(514,2659)(515,2658)(516,2657)(517,2656)(518,2655)(519,2654)(520,2653)(521,2652)(522,2651)(523,2650)(524,2649)(525,2648)(526,2647)(527,2646)(528,2645)(529,2644)(530,2643)(531,2642)(532,2641)(533,2640)(534,2639)(535,2638)(536,2637)(537,2636)(538,2635)(539,2634)(540,2633)(541,2632)(542,2631)(543,2630)(544,2629)(545,2628)(546,2627)(547,2626)(548,2625)(549,2624)(550,2623)(551,2622)(552,2621)(553,2620)(554,2619)(555,2618)(556,2617)(557,2616)(558,2615)(559,2614)(560,2613)(561,2612)(562,2611)(563,2610)(564,2609)(565,2608)(566,2607)(567,2606)(568,2605)(569,2604)(570,2603)(571,2602)(572,2601)(573,2600)(574,2599)(575,2598)(576,2597)(577,2596)(578,2595)(579,2594)(580,2593)(581,2592)(582,2591)(583,2590)(584,2589)(585,2588)(586,2587)(587,2586)(588,2585)(589,2584)(590,2583)(591,2582)(592,2581)(593,2580)(594,2579)(595,2578)(596,2577)(597,2576)(598,2575)(599,2574)(600,2573)(601,2572)(602,2571)(603,2570)(604,2569)(605,2568)(606,2567)(607,2566)(608,2565)(609,2564)(610,2563)(611,2562)(612,2561)(613,2560)(614,2559)(615,2558)(616,2557)(617,2556)(618,2555)(619,2554)(620,2553)(621,2552)(622,2551)(623,2550)(624,2549)(625,2548)(626,2547)(627,2546)(628,2545)(629,2544)(630,2543)(631,2542)(632,2541)(633,2540)(634,2539)(635,2538)(636,2537)(637,2536)(638,2535)(639,2534)(640,2533)(641,2532)(642,2531)(643,2530)(644,2529)(645,2528)(646,2527)(647,2526)(648,2525)(649,2524)(650,2523)(651,2522)(652,2521)(653,2520)(654,2519)(655,2518)(656,2517)(657,2516)(658,2515)(659,2514)(660,2513)(661,2512)(662,2511)(663,2510)(664,2509)(665,2508)(666,2507)(667,2506)(668,2505)(669,2504)(670,2503)(671,2502)(672,2501)(673,2500)(674,2499)(675,2498)(676,2497)(677,2496)(678,2495)(679,2494)(680,2493)(681,2492)(682,2491)(683,2490)(684,2489)(685,2488)(686,2487)(687,2486)(688,2485)(689,2484)(690,2483)(691,2482)(692,2481)(693,2480)(694,2479)(695,2478)(696,2477)(697,2476)(698,2475)(699,2474)(700,2473)(701,2472)(702,2471)(703,2470)(704,2469)(705,2468)(706,2467)(707,2466)(708,2465)(709,2464)(710,2463)(711,2462)(712,2461)(713,2460)(714,2459)(715,2458)(716,2457)(717,2456)(718,2455)(719,2454)(720,2453)(721,2452)(722,2451)(723,2450)(724,2449)(725,2448)(726,2447)(727,2446)(728,2445)(729,2444)(730,2443)(731,2442)(732,2441)(733,2440)(734,2439)(735,2438)(736,2437)(737,2436)(738,2435)(739,2434)(740,2433)(741,2432)(742,2431)(743,2430)(744,2429)(745,2428)(746,2427)(747,2426)(748,2425)(749,2424)(750,2423)(751,2422)(752,2421)(753,2420)(754,2419)(755,2418)(756,2417)(757,2416)(758,2415)(759,2414)(760,2413)(761,2412)(762,2411)(763,2410)(764,2409)(765,2408)(766,2407)(767,2406)(768,2405)(769,2404)(770,2403)(771,2402)(772,2401)(773,2400)(774,2399)(775,2398)(776,2397)(777,2396)(778,2395)(779,2394)(780,2393)(781,2392)(782,2391)(783,2390)(784,2389)(785,2388)(786,2387)(787,2386)(788,2385)(789,2384)(790,2383)(791,2382)(792,2381)(793,2380)(794,2379)(795,2378)(796,2377)(797,2376)(798,2375)(799,2374)(800,2373)(801,2372)(802,2371)(803,2370)(804,2369)(805,2368)(806,2367)(807,2366)(808,2365)(809,2364)(810,2363)(811,2362)(812,2361)(813,2360)(814,2359)(815,2358)(816,2357)(817,2356)(818,2355)(819,2354)(820,2353)(821,2352)(822,2351)(823,2350)(824,2349)(825,2348)(826,2347)(827,2346)(828,2345)(829,2344)(830,2343)(831,2342)(832,2341)(833,2340)(834,2339)(835,2338)(836,2337)(837,2336)(838,2335)(839,2334)(840,2333)(841,2332)(842,2331)(843,2330)(844,2329)(845,2328)(846,2327)(847,2326)(848,2325)(849,2324)(850,2323)(851,2322)(852,2321)(853,2320)(854,2319)(855,2318)(856,2317)(857,2316)(858,2315)(859,2314)(860,2313)(861,2312)(862,2311)(863,2310)(864,2309)(865,2308)(866,2307)(867,2306)(868,2305)(869,2304)(870,2303)(871,2302)(872,2301)(873,2300)(874,2299)(875,2298)(876,2297)(877,2296)(878,2295)(879,2294)(880,2293)(881,2292)(882,2291)(883,2290)(884,2289)(885,2288)(886,2287)(887,2286)(888,2285)(889,2284)(890,2283)(891,2282)(892,2281)(893,2280)(894,2279)(895,2278)(896,2277)(897,2276)(898,2275)(899,2274)(900,2273)(901,2272)(902,2271)(903,2270)(904,2269)(905,2268)(906,2267)(907,2266)(908,2265)(909,2264)(910,2263)(911,2262)(912,2261)(913,2260)(914,2259)(915,2258)(916,2257)(917,2256)(918,2255)(919,2254)(920,2253)(921,2252)(922,2251)(923,2250)(924,2249)(925,2248)(926,2247)(927,2246)(928,2245)(929,2244)(930,2243)(931,2242)(932,2241)(933,2240)(934,2239)(935,2238)(936,2237)(937,2236)(938,2235)(939,2234)(940,2233)(941,2232)(942,2231)(943,2230)(944,2229)(945,2228)(946,2227)(947,2226)(948,2225)(949,2224)(950,2223)(951,2222)(952,2221)(953,2220)(954,2219)(955,2218)(956,2217)(957,2216)(958,2215)(959,2214)(960,2213)(961,2212)(962,2211)(963,2210)(964,2209)(965,2208)(966,2207)(967,2206)(968,2205)(969,2204)(970,2203)(971,2202)(972,2201)(973,2200)(974,2199)(975,2198)(976,2197)(977,2196)(978,2195)(979,2194)(980,2193)(981,2192)(982,2191)(983,2190)(984,2189)(985,2188)(986,2187)(987,2186)(988,2185)(989,2184)(990,2183)(991,2182)(992,2181)(993,2180)(994,2179)(995,2178)(996,2177)(997,2176)(998,2175)(999,2174)(1000,2173)(1001,2172)(1002,2171)(1003,2170)(1004,2169)(1005,2168)(1006,2167)(1007,2166)(1008,2165)(1009,2164)(1010,2163)(1011,2162)(1012,2161)(1013,2160)(1014,2159)(1015,2158)(1016,2157)(1017,2156)(1018,2155)(1019,2154)(1020,2153)(1021,2152)(1022,2151)(1023,2150)(1024,2149)(1025,2148)(1026,2147)(1027,2146)(1028,2145)(1029,2144)(1030,2143)(1031,2142)(1032,2141)(1033,2140)(1034,2139)(1035,2138)(1036,2137)(1037,2136)(1038,2135)(1039,2134)(1040,2133)(1041,2132)(1042,2131)(1043,2130)(1044,2129)(1045,2128)(1046,2127)(1047,2126)(1048,2125)(1049,2124)(1050,2123)(1051,2122)(1052,2121)(1053,2120)(1054,2119)(1055,2118)(1056,2117)(1057,2116)(1058,2115)(1059,2114)(1060,2113)(1061,2112)(1062,2111)(1063,2110)(1064,2109)(1065,2108)(1066,2107)(1067,2106)(1068,2105)(1069,2104)(1070,2103)(1071,2102)(1072,2101)(1073,2100)(1074,2099)(1075,2098)(1076,2097)(1077,2096)(1078,2095)(1079,2094)(1080,2093)(1081,2092)(1082,2091)(1083,2090)(1084,2089)(1085,2088)(1086,2087)(1087,2086)(1088,2085)(1089,2084)(1090,2083)(1091,2082)(1092,2081)(1093,2080)(1094,2079)(1095,2078)(1096,2077)(1097,2076)(1098,2075)(1099,2074)(1100,2073)(1101,2072)(1102,2071)(1103,2070)(1104,2069)(1105,2068)(1106,2067)(1107,2066)(1108,2065)(1109,2064)(1110,2063)(1111,2062)(1112,2061)(1113,2060)(1114,2059)(1115,2058)(1116,2057)(1117,2056)(1118,2055)(1119,2054)(1120,2053)(1121,2052)(1122,2051)(1123,2050)(1124,2049)(1125,2048)(1126,2047)(1127,2046)(1128,2045)(1129,2044)(1130,2043)(1131,2042)(1132,2041)(1133,2040)(1134,2039)(1135,2038)(1136,2037)(1137,2036)(1138,2035)(1139,2034)(1140,2033)(1141,2032)(1142,2031)(1143,2030)(1144,2029)(1145,2028)(1146,2027)(1147,2026)(1148,2025)(1149,2024)(1150,2023)(1151,2022)(1152,2021)(1153,2020)(1154,2019)(1155,2018)(1156,2017)(1157,2016)(1158,2015)(1159,2014)(1160,2013)(1161,2012)(1162,2011)(1163,2010)(1164,2009)(1165,2008)(1166,2007)(1167,2006)(1168,2005)(1169,2004)(1170,2003)(1171,2002)(1172,2001)(1173,2000)(1174,1999)(1175,1998)(1176,1997)(1177,1996)(1178,1995)(1179,1994)(1180,1993)(1181,1992)(1182,1991)(1183,1990)(1184,1989)(1185,1988)(1186,1987)(1187,1986)(1188,1985)(1189,1984)(1190,1983)(1191,1982)(1192,1981)(1193,1980)(1194,1979)(1195,1978)(1196,1977)(1197,1976)(1198,1975)(1199,1974)(1200,1973)(1201,1972)(1202,1971)(1203,1970)(1204,1969)(1205,1968)(1206,1967)(1207,1966)(1208,1965)(1209,1964)(1210,1963)(1211,1962)(1212,1961)(1213,1960)(1214,1959)(1215,1958)(1216,1957)(1217,1956)(1218,1955)(1219,1954)(1220,1953)(1221,1952)(1222,1951)(1223,1950)(1224,1949)(1225,1948)(1226,1947)(1227,1946)(1228,1945)(1229,1944)(1230,1943)(1231,1942)(1232,1941)(1233,1940)(1234,1939)(1235,1938)(1236,1937)(1237,1936)(1238,1935)(1239,1934)(1240,1933)(1241,1932)(1242,1931)(1243,1930)(1244,1929)(1245,1928)(1246,1927)(1247,1926)(1248,1925)(1249,1924)(1250,1923)(1251,1922)(1252,1921)(1253,1920)(1254,1919)(1255,1918)(1256,1917)(1257,1916)(1258,1915)(1259,1914)(1260,1913)(1261,1912)(1262,1911)(1263,1910)(1264,1909)(1265,1908)(1266,1907)(1267,1906)(1268,1905)(1269,1904)(1270,1903)(1271,1902)(1272,1901)(1273,1900)(1274,1899)(1275,1898)(1276,1897)(1277,1896)(1278,1895)(1279,1894)(1280,1893)(1281,1892)(1282,1891)(1283,1890)(1284,1889)(1285,1888)(1286,1887)(1287,1886)(1288,1885)(1289,1884)(1290,1883)(1291,1882)(1292,1881)(1293,1880)(1294,1879)(1295,1878)(1296,1877)(1297,1876)(1298,1875)(1299,1874)(1300,1873)(1301,1872)(1302,1871)(1303,1870)(1304,1869)(1305,1868)(1306,1867)(1307,1866)(1308,1865)(1309,1864)(1310,1863)(1311,1862)(1312,1861)(1313,1860)(1314,1859)(1315,1858)(1316,1857)(1317,1856)(1318,1855)(1319,1854)(1320,1853)(1321,1852)(1322,1851)(1323,1850)(1324,1849)(1325,1848)(1326,1847)(1327,1846)(1328,1845)(1329,1844)(1330,1843)(1331,1842)(1332,1841)(1333,1840)(1334,1839)(1335,1838)(1336,1837)(1337,1836)(1338,1835)(1339,1834)(1340,1833)(1341,1832)(1342,1831)(1343,1830)(1344,1829)(1345,1828)(1346,1827)(1347,1826)(1348,1825)(1349,1824)(1350,1823)(1351,1822)(1352,1821)(1353,1820)(1354,1819)(1355,1818)(1356,1817)(1357,1816)(1358,1815)(1359,1814)(1360,1813)(1361,1812)(1362,1811)(1363,1810)(1364,1809)(1365,1808)(1366,1807)(1367,1806)(1368,1805)(1369,1804)(1370,1803)(1371,1802)(1372,1801)(1373,1800)(1374,1799)(1375,1798)(1376,1797)(1377,1796)(1378,1795)(1379,1794)(1380,1793)(1381,1792)(1382,1791)(1383,1790)(1384,1789)(1385,1788)(1386,1787)(1387,1786)(1388,1785)(1389,1784)(1390,1783)(1391,1782)(1392,1781)(1393,1780)(1394,1779)(1395,1778)(1396,1777)(1397,1776)(1398,1775)(1399,1774)(1400,1773)(1401,1772)(1402,1771)(1403,1770)(1404,1769)(1405,1768)(1406,1767)(1407,1766)(1408,1765)(1409,1764)(1410,1763)(1411,1762)(1412,1761)(1413,1760)(1414,1759)(1415,1758)(1416,1757)(1417,1756)(1418,1755)(1419,1754)(1420,1753)(1421,1752)(1422,1751)(1423,1750)(1424,1749)(1425,1748)(1426,1747)(1427,1746)(1428,1745)(1429,1744)(1430,1743)(1431,1742)(1432,1741)(1433,1740)(1434,1739)(1435,1738)(1436,1737)(1437,1736)(1438,1735)(1439,1734)(1440,1733)(1441,1732)(1442,1731)(1443,1730)(1444,1729)(1445,1728)(1446,1727)(1447,1726)(1448,1725)(1449,1724)(1450,1723)(1451,1722)(1452,1721)(1453,1720)(1454,1719)(1455,1718)(1456,1717)(1457,1716)(1458,1715)(1459,1714)(1460,1713)(1461,1712)(1462,1711)(1463,1710)(1464,1709)(1465,1708)(1466,1707)(1467,1706)(1468,1705)(1469,1704)(1470,1703)(1471,1702)(1472,1701)(1473,1700)(1474,1699)(1475,1698)(1476,1697)(1477,1696)(1478,1695)(1479,1694)(1480,1693)(1481,1692)(1482,1691)(1483,1690)(1484,1689)(1485,1688)(1486,1687)(1487,1686)(1488,1685)(1489,1684)(1490,1683)(1491,1682)(1492,1681)(1493,1680)(1494,1679)(1495,1678)(1496,1677)(1497,1676)(1498,1675)(1499,1674)(1500,1673)(1501,1672)(1502,1671)(1503,1670)(1504,1669)(1505,1668)(1506,1667)(1507,1666)(1508,1665)(1509,1664)(1510,1663)(1511,1662)(1512,1661)(1513,1660)(1514,1659)(1515,1658)(1516,1657)(1517,1656)(1518,1655)(1519,1654)(1520,1653)(1521,1652)(1522,1651)(1523,1650)(1524,1649)(1525,1648)(1526,1647)(1527,1646)(1528,1645)(1529,1644)(1530,1643)(1531,1642)(1532,1641)(1533,1640)(1534,1639)(1535,1638)(1536,1637)(1537,1636)(1538,1635)(1539,1634)(1540,1633)(1541,1632)(1542,1631)(1543,1630)(1544,1629)(1545,1628)(1546,1627)(1547,1626)(1548,1625)(1549,1624)(1550,1623)(1551,1622)(1552,1621)(1553,1620)(1554,1619)(1555,1618)(1556,1617)(1557,1616)(1558,1615)(1559,1614)(1560,1613)(1561,1612)(1562,1611)(1563,1610)(1564,1609)(1565,1608)(1566,1607)(1567,1606)(1568,1605)(1569,1604)(1570,1603)(1571,1602)(1572,1601)(1573,1600)(1574,1599)(1575,1598)(1576,1597)(1577,1596)(1578,1595)(1579,1594)(1580,1593)(1581,1592)(1582,1591)(1583,1590)(1584,1589)(1585,1588)(1586,1587)

Polycyclic presentation:

2^3,3163|b^a=bc,d^a=d^3162,d^b=d^3162

Conjugacy classes & character table

6329 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25304, 10);