Finite Group Databasebeta

?

← Prev (#37557297) Next (#37557299) →

D₁₁₈₅₂ #37557298

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

Polycyclic presentation:

2^3,2963|b^a=bc,d^a=d^2962,d^b=d^2962

Conjugacy classes & character table

5929 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23704, 10);