Finite Group Databasebeta

?

← Prev (#46853257) Next (#46853259) →

Dic₈₇₂₇ #46853258

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

Polycyclic presentation:

2,3,2909,2|a^2=d,b^a=b^2,c^a=c^2908

Conjugacy classes & character table

8730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34908, 4);