Finite Group Databasebeta

?

← Prev (#49087182) Next (#49087184) →

Dic₈₉₁₃ #49087183

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2,3,2971,2|a^2=d,b^a=b^2,c^a=c^2970

Conjugacy classes & character table

8916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35652, 6);