Finite Group Databasebeta

?

← Prev (#40999453) Next (#40999455) →

Dic₆₆₉₄ #40999454

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

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 3355 points:

(1,2,3,4)(5,8,7,6)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,2721,2722,2723,2724,2725,2726,2727,2728,2729,2730,2731,2732,2733,2734,2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,2751,2752,2753,2754,2755,2756,2757,2758,2759,2760,2761,2762,2763,2764,2765,2766,2767,2768,2769,2770,2771,2772,2773,2774,2775,2776,2777,2778,2779,2780,2781,2782,2783,2784,2785,2786,2787,2788,2789,2790,2791,2792,2793,2794,2795,2796,2797,2798,2799,2800,2801,2802,2803,2804,2805,2806,2807,2808,2809,2810,2811,2812,2813,2814,2815,2816,2817,2818,2819,2820,2821,2822,2823,2824,2825,2826,2827,2828,2829,2830,2831,2832,2833,2834,2835,2836,2837,2838,2839,2840,2841,2842,2843,2844,2845,2846,2847,2848,2849,2850,2851,2852,2853,2854,2855,2856,2857,2858,2859,2860,2861,2862,2863,2864,2865,2866,2867,2868,2869,2870,2871,2872,2873,2874,2875,2876,2877,2878,2879,2880,2881,2882,2883,2884,2885,2886,2887,2888,2889,2890,2891,2892,2893,2894,2895,2896,2897,2898,2899,2900,2901,2902,2903,2904,2905,2906,2907,2908,2909,2910,2911,2912,2913,2914,2915,2916,2917,2918,2919,2920,2921,2922,2923,2924,2925,2926,2927,2928,2929,2930,2931,2932,2933,2934,2935,2936,2937,2938,2939,2940,2941,2942,2943,2944,2945,2946,2947,2948,2949,2950,2951,2952,2953,2954,2955,2956,2957,2958,2959,2960,2961,2962,2963,2964,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,2977,2978,2979,2980,2981,2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003,3004,3005,3006,3007,3008,3009,3010,3011,3012,3013,3014,3015,3016,3017,3018,3019,3020,3021,3022,3023,3024,3025,3026,3027,3028,3029,3030,3031,3032,3033,3034,3035,3036,3037,3038,3039,3040,3041,3042,3043,3044,3045,3046,3047,3048,3049,3050,3051,3052,3053,3054,3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,3067,3068,3069,3070,3071,3072,3073,3074,3075,3076,3077,3078,3079,3080,3081,3082,3083,3084,3085,3086,3087,3088,3089,3090,3091,3092,3093,3094,3095,3096,3097,3098,3099,3100,3101,3102,3103,3104,3105,3106,3107,3108,3109,3110,3111,3112,3113,3114,3115,3116,3117,3118,3119,3120,3121,3122,3123,3124,3125,3126,3127,3128,3129,3130,3131,3132,3133,3134,3135,3136,3137,3138,3139,3140,3141,3142,3143,3144,3145,3146,3147,3148,3149,3150,3151,3152,3153,3154,3155,3156,3157,3158,3159,3160,3161,3162,3163,3164,3165,3166,3167,3168,3169,3170,3171,3172,3173,3174,3175,3176,3177,3178,3179,3180,3181,3182,3183,3184,3185,3186,3187,3188,3189,3190,3191,3192,3193,3194,3195,3196,3197,3198,3199,3200,3201,3202,3203,3204,3205,3206,3207,3208,3209,3210,3211,3212,3213,3214,3215,3216,3217,3218,3219,3220,3221,3222,3223,3224,3225,3226,3227,3228,3229,3230,3231,3232,3233,3234,3235,3236,3237,3238,3239,3240,3241,3242,3243,3244,3245,3246,3247,3248,3249,3250,3251,3252,3253,3254,3255,3256,3257,3258,3259,3260,3261,3262,3263,3264,3265,3266,3267,3268,3269,3270,3271,3272,3273,3274,3275,3276,3277,3278,3279,3280,3281,3282,3283,3284,3285,3286,3287,3288,3289,3290,3291,3292,3293,3294,3295,3296,3297,3298,3299,3300,3301,3302,3303,3304,3305,3306,3307,3308,3309,3310,3311,3312,3313,3314,3315,3316,3317,3318,3319,3320,3321,3322,3323,3324,3325,3326,3327,3328,3329,3330,3331,3332,3333,3334,3335,3336,3337,3338,3339,3340,3341,3342,3343,3344,3345,3346,3347,3348,3349,3350,3351,3352,3353,3354,3355);(1,5,3,7)(2,6,4,8)(10,3355)(11,3354)(12,3353)(13,3352)(14,3351)(15,3350)(16,3349)(17,3348)(18,3347)(19,3346)(20,3345)(21,3344)(22,3343)(23,3342)(24,3341)(25,3340)(26,3339)(27,3338)(28,3337)(29,3336)(30,3335)(31,3334)(32,3333)(33,3332)(34,3331)(35,3330)(36,3329)(37,3328)(38,3327)(39,3326)(40,3325)(41,3324)(42,3323)(43,3322)(44,3321)(45,3320)(46,3319)(47,3318)(48,3317)(49,3316)(50,3315)(51,3314)(52,3313)(53,3312)(54,3311)(55,3310)(56,3309)(57,3308)(58,3307)(59,3306)(60,3305)(61,3304)(62,3303)(63,3302)(64,3301)(65,3300)(66,3299)(67,3298)(68,3297)(69,3296)(70,3295)(71,3294)(72,3293)(73,3292)(74,3291)(75,3290)(76,3289)(77,3288)(78,3287)(79,3286)(80,3285)(81,3284)(82,3283)(83,3282)(84,3281)(85,3280)(86,3279)(87,3278)(88,3277)(89,3276)(90,3275)(91,3274)(92,3273)(93,3272)(94,3271)(95,3270)(96,3269)(97,3268)(98,3267)(99,3266)(100,3265)(101,3264)(102,3263)(103,3262)(104,3261)(105,3260)(106,3259)(107,3258)(108,3257)(109,3256)(110,3255)(111,3254)(112,3253)(113,3252)(114,3251)(115,3250)(116,3249)(117,3248)(118,3247)(119,3246)(120,3245)(121,3244)(122,3243)(123,3242)(124,3241)(125,3240)(126,3239)(127,3238)(128,3237)(129,3236)(130,3235)(131,3234)(132,3233)(133,3232)(134,3231)(135,3230)(136,3229)(137,3228)(138,3227)(139,3226)(140,3225)(141,3224)(142,3223)(143,3222)(144,3221)(145,3220)(146,3219)(147,3218)(148,3217)(149,3216)(150,3215)(151,3214)(152,3213)(153,3212)(154,3211)(155,3210)(156,3209)(157,3208)(158,3207)(159,3206)(160,3205)(161,3204)(162,3203)(163,3202)(164,3201)(165,3200)(166,3199)(167,3198)(168,3197)(169,3196)(170,3195)(171,3194)(172,3193)(173,3192)(174,3191)(175,3190)(176,3189)(177,3188)(178,3187)(179,3186)(180,3185)(181,3184)(182,3183)(183,3182)(184,3181)(185,3180)(186,3179)(187,3178)(188,3177)(189,3176)(190,3175)(191,3174)(192,3173)(193,3172)(194,3171)(195,3170)(196,3169)(197,3168)(198,3167)(199,3166)(200,3165)(201,3164)(202,3163)(203,3162)(204,3161)(205,3160)(206,3159)(207,3158)(208,3157)(209,3156)(210,3155)(211,3154)(212,3153)(213,3152)(214,3151)(215,3150)(216,3149)(217,3148)(218,3147)(219,3146)(220,3145)(221,3144)(222,3143)(223,3142)(224,3141)(225,3140)(226,3139)(227,3138)(228,3137)(229,3136)(230,3135)(231,3134)(232,3133)(233,3132)(234,3131)(235,3130)(236,3129)(237,3128)(238,3127)(239,3126)(240,3125)(241,3124)(242,3123)(243,3122)(244,3121)(245,3120)(246,3119)(247,3118)(248,3117)(249,3116)(250,3115)(251,3114)(252,3113)(253,3112)(254,3111)(255,3110)(256,3109)(257,3108)(258,3107)(259,3106)(260,3105)(261,3104)(262,3103)(263,3102)(264,3101)(265,3100)(266,3099)(267,3098)(268,3097)(269,3096)(270,3095)(271,3094)(272,3093)(273,3092)(274,3091)(275,3090)(276,3089)(277,3088)(278,3087)(279,3086)(280,3085)(281,3084)(282,3083)(283,3082)(284,3081)(285,3080)(286,3079)(287,3078)(288,3077)(289,3076)(290,3075)(291,3074)(292,3073)(293,3072)(294,3071)(295,3070)(296,3069)(297,3068)(298,3067)(299,3066)(300,3065)(301,3064)(302,3063)(303,3062)(304,3061)(305,3060)(306,3059)(307,3058)(308,3057)(309,3056)(310,3055)(311,3054)(312,3053)(313,3052)(314,3051)(315,3050)(316,3049)(317,3048)(318,3047)(319,3046)(320,3045)(321,3044)(322,3043)(323,3042)(324,3041)(325,3040)(326,3039)(327,3038)(328,3037)(329,3036)(330,3035)(331,3034)(332,3033)(333,3032)(334,3031)(335,3030)(336,3029)(337,3028)(338,3027)(339,3026)(340,3025)(341,3024)(342,3023)(343,3022)(344,3021)(345,3020)(346,3019)(347,3018)(348,3017)(349,3016)(350,3015)(351,3014)(352,3013)(353,3012)(354,3011)(355,3010)(356,3009)(357,3008)(358,3007)(359,3006)(360,3005)(361,3004)(362,3003)(363,3002)(364,3001)(365,3000)(366,2999)(367,2998)(368,2997)(369,2996)(370,2995)(371,2994)(372,2993)(373,2992)(374,2991)(375,2990)(376,2989)(377,2988)(378,2987)(379,2986)(380,2985)(381,2984)(382,2983)(383,2982)(384,2981)(385,2980)(386,2979)(387,2978)(388,2977)(389,2976)(390,2975)(391,2974)(392,2973)(393,2972)(394,2971)(395,2970)(396,2969)(397,2968)(398,2967)(399,2966)(400,2965)(401,2964)(402,2963)(403,2962)(404,2961)(405,2960)(406,2959)(407,2958)(408,2957)(409,2956)(410,2955)(411,2954)(412,2953)(413,2952)(414,2951)(415,2950)(416,2949)(417,2948)(418,2947)(419,2946)(420,2945)(421,2944)(422,2943)(423,2942)(424,2941)(425,2940)(426,2939)(427,2938)(428,2937)(429,2936)(430,2935)(431,2934)(432,2933)(433,2932)(434,2931)(435,2930)(436,2929)(437,2928)(438,2927)(439,2926)(440,2925)(441,2924)(442,2923)(443,2922)(444,2921)(445,2920)(446,2919)(447,2918)(448,2917)(449,2916)(450,2915)(451,2914)(452,2913)(453,2912)(454,2911)(455,2910)(456,2909)(457,2908)(458,2907)(459,2906)(460,2905)(461,2904)(462,2903)(463,2902)(464,2901)(465,2900)(466,2899)(467,2898)(468,2897)(469,2896)(470,2895)(471,2894)(472,2893)(473,2892)(474,2891)(475,2890)(476,2889)(477,2888)(478,2887)(479,2886)(480,2885)(481,2884)(482,2883)(483,2882)(484,2881)(485,2880)(486,2879)(487,2878)(488,2877)(489,2876)(490,2875)(491,2874)(492,2873)(493,2872)(494,2871)(495,2870)(496,2869)(497,2868)(498,2867)(499,2866)(500,2865)(501,2864)(502,2863)(503,2862)(504,2861)(505,2860)(506,2859)(507,2858)(508,2857)(509,2856)(510,2855)(511,2854)(512,2853)(513,2852)(514,2851)(515,2850)(516,2849)(517,2848)(518,2847)(519,2846)(520,2845)(521,2844)(522,2843)(523,2842)(524,2841)(525,2840)(526,2839)(527,2838)(528,2837)(529,2836)(530,2835)(531,2834)(532,2833)(533,2832)(534,2831)(535,2830)(536,2829)(537,2828)(538,2827)(539,2826)(540,2825)(541,2824)(542,2823)(543,2822)(544,2821)(545,2820)(546,2819)(547,2818)(548,2817)(549,2816)(550,2815)(551,2814)(552,2813)(553,2812)(554,2811)(555,2810)(556,2809)(557,2808)(558,2807)(559,2806)(560,2805)(561,2804)(562,2803)(563,2802)(564,2801)(565,2800)(566,2799)(567,2798)(568,2797)(569,2796)(570,2795)(571,2794)(572,2793)(573,2792)(574,2791)(575,2790)(576,2789)(577,2788)(578,2787)(579,2786)(580,2785)(581,2784)(582,2783)(583,2782)(584,2781)(585,2780)(586,2779)(587,2778)(588,2777)(589,2776)(590,2775)(591,2774)(592,2773)(593,2772)(594,2771)(595,2770)(596,2769)(597,2768)(598,2767)(599,2766)(600,2765)(601,2764)(602,2763)(603,2762)(604,2761)(605,2760)(606,2759)(607,2758)(608,2757)(609,2756)(610,2755)(611,2754)(612,2753)(613,2752)(614,2751)(615,2750)(616,2749)(617,2748)(618,2747)(619,2746)(620,2745)(621,2744)(622,2743)(623,2742)(624,2741)(625,2740)(626,2739)(627,2738)(628,2737)(629,2736)(630,2735)(631,2734)(632,2733)(633,2732)(634,2731)(635,2730)(636,2729)(637,2728)(638,2727)(639,2726)(640,2725)(641,2724)(642,2723)(643,2722)(644,2721)(645,2720)(646,2719)(647,2718)(648,2717)(649,2716)(650,2715)(651,2714)(652,2713)(653,2712)(654,2711)(655,2710)(656,2709)(657,2708)(658,2707)(659,2706)(660,2705)(661,2704)(662,2703)(663,2702)(664,2701)(665,2700)(666,2699)(667,2698)(668,2697)(669,2696)(670,2695)(671,2694)(672,2693)(673,2692)(674,2691)(675,2690)(676,2689)(677,2688)(678,2687)(679,2686)(680,2685)(681,2684)(682,2683)(683,2682)(684,2681)(685,2680)(686,2679)(687,2678)(688,2677)(689,2676)(690,2675)(691,2674)(692,2673)(693,2672)(694,2671)(695,2670)(696,2669)(697,2668)(698,2667)(699,2666)(700,2665)(701,2664)(702,2663)(703,2662)(704,2661)(705,2660)(706,2659)(707,2658)(708,2657)(709,2656)(710,2655)(711,2654)(712,2653)(713,2652)(714,2651)(715,2650)(716,2649)(717,2648)(718,2647)(719,2646)(720,2645)(721,2644)(722,2643)(723,2642)(724,2641)(725,2640)(726,2639)(727,2638)(728,2637)(729,2636)(730,2635)(731,2634)(732,2633)(733,2632)(734,2631)(735,2630)(736,2629)(737,2628)(738,2627)(739,2626)(740,2625)(741,2624)(742,2623)(743,2622)(744,2621)(745,2620)(746,2619)(747,2618)(748,2617)(749,2616)(750,2615)(751,2614)(752,2613)(753,2612)(754,2611)(755,2610)(756,2609)(757,2608)(758,2607)(759,2606)(760,2605)(761,2604)(762,2603)(763,2602)(764,2601)(765,2600)(766,2599)(767,2598)(768,2597)(769,2596)(770,2595)(771,2594)(772,2593)(773,2592)(774,2591)(775,2590)(776,2589)(777,2588)(778,2587)(779,2586)(780,2585)(781,2584)(782,2583)(783,2582)(784,2581)(785,2580)(786,2579)(787,2578)(788,2577)(789,2576)(790,2575)(791,2574)(792,2573)(793,2572)(794,2571)(795,2570)(796,2569)(797,2568)(798,2567)(799,2566)(800,2565)(801,2564)(802,2563)(803,2562)(804,2561)(805,2560)(806,2559)(807,2558)(808,2557)(809,2556)(810,2555)(811,2554)(812,2553)(813,2552)(814,2551)(815,2550)(816,2549)(817,2548)(818,2547)(819,2546)(820,2545)(821,2544)(822,2543)(823,2542)(824,2541)(825,2540)(826,2539)(827,2538)(828,2537)(829,2536)(830,2535)(831,2534)(832,2533)(833,2532)(834,2531)(835,2530)(836,2529)(837,2528)(838,2527)(839,2526)(840,2525)(841,2524)(842,2523)(843,2522)(844,2521)(845,2520)(846,2519)(847,2518)(848,2517)(849,2516)(850,2515)(851,2514)(852,2513)(853,2512)(854,2511)(855,2510)(856,2509)(857,2508)(858,2507)(859,2506)(860,2505)(861,2504)(862,2503)(863,2502)(864,2501)(865,2500)(866,2499)(867,2498)(868,2497)(869,2496)(870,2495)(871,2494)(872,2493)(873,2492)(874,2491)(875,2490)(876,2489)(877,2488)(878,2487)(879,2486)(880,2485)(881,2484)(882,2483)(883,2482)(884,2481)(885,2480)(886,2479)(887,2478)(888,2477)(889,2476)(890,2475)(891,2474)(892,2473)(893,2472)(894,2471)(895,2470)(896,2469)(897,2468)(898,2467)(899,2466)(900,2465)(901,2464)(902,2463)(903,2462)(904,2461)(905,2460)(906,2459)(907,2458)(908,2457)(909,2456)(910,2455)(911,2454)(912,2453)(913,2452)(914,2451)(915,2450)(916,2449)(917,2448)(918,2447)(919,2446)(920,2445)(921,2444)(922,2443)(923,2442)(924,2441)(925,2440)(926,2439)(927,2438)(928,2437)(929,2436)(930,2435)(931,2434)(932,2433)(933,2432)(934,2431)(935,2430)(936,2429)(937,2428)(938,2427)(939,2426)(940,2425)(941,2424)(942,2423)(943,2422)(944,2421)(945,2420)(946,2419)(947,2418)(948,2417)(949,2416)(950,2415)(951,2414)(952,2413)(953,2412)(954,2411)(955,2410)(956,2409)(957,2408)(958,2407)(959,2406)(960,2405)(961,2404)(962,2403)(963,2402)(964,2401)(965,2400)(966,2399)(967,2398)(968,2397)(969,2396)(970,2395)(971,2394)(972,2393)(973,2392)(974,2391)(975,2390)(976,2389)(977,2388)(978,2387)(979,2386)(980,2385)(981,2384)(982,2383)(983,2382)(984,2381)(985,2380)(986,2379)(987,2378)(988,2377)(989,2376)(990,2375)(991,2374)(992,2373)(993,2372)(994,2371)(995,2370)(996,2369)(997,2368)(998,2367)(999,2366)(1000,2365)(1001,2364)(1002,2363)(1003,2362)(1004,2361)(1005,2360)(1006,2359)(1007,2358)(1008,2357)(1009,2356)(1010,2355)(1011,2354)(1012,2353)(1013,2352)(1014,2351)(1015,2350)(1016,2349)(1017,2348)(1018,2347)(1019,2346)(1020,2345)(1021,2344)(1022,2343)(1023,2342)(1024,2341)(1025,2340)(1026,2339)(1027,2338)(1028,2337)(1029,2336)(1030,2335)(1031,2334)(1032,2333)(1033,2332)(1034,2331)(1035,2330)(1036,2329)(1037,2328)(1038,2327)(1039,2326)(1040,2325)(1041,2324)(1042,2323)(1043,2322)(1044,2321)(1045,2320)(1046,2319)(1047,2318)(1048,2317)(1049,2316)(1050,2315)(1051,2314)(1052,2313)(1053,2312)(1054,2311)(1055,2310)(1056,2309)(1057,2308)(1058,2307)(1059,2306)(1060,2305)(1061,2304)(1062,2303)(1063,2302)(1064,2301)(1065,2300)(1066,2299)(1067,2298)(1068,2297)(1069,2296)(1070,2295)(1071,2294)(1072,2293)(1073,2292)(1074,2291)(1075,2290)(1076,2289)(1077,2288)(1078,2287)(1079,2286)(1080,2285)(1081,2284)(1082,2283)(1083,2282)(1084,2281)(1085,2280)(1086,2279)(1087,2278)(1088,2277)(1089,2276)(1090,2275)(1091,2274)(1092,2273)(1093,2272)(1094,2271)(1095,2270)(1096,2269)(1097,2268)(1098,2267)(1099,2266)(1100,2265)(1101,2264)(1102,2263)(1103,2262)(1104,2261)(1105,2260)(1106,2259)(1107,2258)(1108,2257)(1109,2256)(1110,2255)(1111,2254)(1112,2253)(1113,2252)(1114,2251)(1115,2250)(1116,2249)(1117,2248)(1118,2247)(1119,2246)(1120,2245)(1121,2244)(1122,2243)(1123,2242)(1124,2241)(1125,2240)(1126,2239)(1127,2238)(1128,2237)(1129,2236)(1130,2235)(1131,2234)(1132,2233)(1133,2232)(1134,2231)(1135,2230)(1136,2229)(1137,2228)(1138,2227)(1139,2226)(1140,2225)(1141,2224)(1142,2223)(1143,2222)(1144,2221)(1145,2220)(1146,2219)(1147,2218)(1148,2217)(1149,2216)(1150,2215)(1151,2214)(1152,2213)(1153,2212)(1154,2211)(1155,2210)(1156,2209)(1157,2208)(1158,2207)(1159,2206)(1160,2205)(1161,2204)(1162,2203)(1163,2202)(1164,2201)(1165,2200)(1166,2199)(1167,2198)(1168,2197)(1169,2196)(1170,2195)(1171,2194)(1172,2193)(1173,2192)(1174,2191)(1175,2190)(1176,2189)(1177,2188)(1178,2187)(1179,2186)(1180,2185)(1181,2184)(1182,2183)(1183,2182)(1184,2181)(1185,2180)(1186,2179)(1187,2178)(1188,2177)(1189,2176)(1190,2175)(1191,2174)(1192,2173)(1193,2172)(1194,2171)(1195,2170)(1196,2169)(1197,2168)(1198,2167)(1199,2166)(1200,2165)(1201,2164)(1202,2163)(1203,2162)(1204,2161)(1205,2160)(1206,2159)(1207,2158)(1208,2157)(1209,2156)(1210,2155)(1211,2154)(1212,2153)(1213,2152)(1214,2151)(1215,2150)(1216,2149)(1217,2148)(1218,2147)(1219,2146)(1220,2145)(1221,2144)(1222,2143)(1223,2142)(1224,2141)(1225,2140)(1226,2139)(1227,2138)(1228,2137)(1229,2136)(1230,2135)(1231,2134)(1232,2133)(1233,2132)(1234,2131)(1235,2130)(1236,2129)(1237,2128)(1238,2127)(1239,2126)(1240,2125)(1241,2124)(1242,2123)(1243,2122)(1244,2121)(1245,2120)(1246,2119)(1247,2118)(1248,2117)(1249,2116)(1250,2115)(1251,2114)(1252,2113)(1253,2112)(1254,2111)(1255,2110)(1256,2109)(1257,2108)(1258,2107)(1259,2106)(1260,2105)(1261,2104)(1262,2103)(1263,2102)(1264,2101)(1265,2100)(1266,2099)(1267,2098)(1268,2097)(1269,2096)(1270,2095)(1271,2094)(1272,2093)(1273,2092)(1274,2091)(1275,2090)(1276,2089)(1277,2088)(1278,2087)(1279,2086)(1280,2085)(1281,2084)(1282,2083)(1283,2082)(1284,2081)(1285,2080)(1286,2079)(1287,2078)(1288,2077)(1289,2076)(1290,2075)(1291,2074)(1292,2073)(1293,2072)(1294,2071)(1295,2070)(1296,2069)(1297,2068)(1298,2067)(1299,2066)(1300,2065)(1301,2064)(1302,2063)(1303,2062)(1304,2061)(1305,2060)(1306,2059)(1307,2058)(1308,2057)(1309,2056)(1310,2055)(1311,2054)(1312,2053)(1313,2052)(1314,2051)(1315,2050)(1316,2049)(1317,2048)(1318,2047)(1319,2046)(1320,2045)(1321,2044)(1322,2043)(1323,2042)(1324,2041)(1325,2040)(1326,2039)(1327,2038)(1328,2037)(1329,2036)(1330,2035)(1331,2034)(1332,2033)(1333,2032)(1334,2031)(1335,2030)(1336,2029)(1337,2028)(1338,2027)(1339,2026)(1340,2025)(1341,2024)(1342,2023)(1343,2022)(1344,2021)(1345,2020)(1346,2019)(1347,2018)(1348,2017)(1349,2016)(1350,2015)(1351,2014)(1352,2013)(1353,2012)(1354,2011)(1355,2010)(1356,2009)(1357,2008)(1358,2007)(1359,2006)(1360,2005)(1361,2004)(1362,2003)(1363,2002)(1364,2001)(1365,2000)(1366,1999)(1367,1998)(1368,1997)(1369,1996)(1370,1995)(1371,1994)(1372,1993)(1373,1992)(1374,1991)(1375,1990)(1376,1989)(1377,1988)(1378,1987)(1379,1986)(1380,1985)(1381,1984)(1382,1983)(1383,1982)(1384,1981)(1385,1980)(1386,1979)(1387,1978)(1388,1977)(1389,1976)(1390,1975)(1391,1974)(1392,1973)(1393,1972)(1394,1971)(1395,1970)(1396,1969)(1397,1968)(1398,1967)(1399,1966)(1400,1965)(1401,1964)(1402,1963)(1403,1962)(1404,1961)(1405,1960)(1406,1959)(1407,1958)(1408,1957)(1409,1956)(1410,1955)(1411,1954)(1412,1953)(1413,1952)(1414,1951)(1415,1950)(1416,1949)(1417,1948)(1418,1947)(1419,1946)(1420,1945)(1421,1944)(1422,1943)(1423,1942)(1424,1941)(1425,1940)(1426,1939)(1427,1938)(1428,1937)(1429,1936)(1430,1935)(1431,1934)(1432,1933)(1433,1932)(1434,1931)(1435,1930)(1436,1929)(1437,1928)(1438,1927)(1439,1926)(1440,1925)(1441,1924)(1442,1923)(1443,1922)(1444,1921)(1445,1920)(1446,1919)(1447,1918)(1448,1917)(1449,1916)(1450,1915)(1451,1914)(1452,1913)(1453,1912)(1454,1911)(1455,1910)(1456,1909)(1457,1908)(1458,1907)(1459,1906)(1460,1905)(1461,1904)(1462,1903)(1463,1902)(1464,1901)(1465,1900)(1466,1899)(1467,1898)(1468,1897)(1469,1896)(1470,1895)(1471,1894)(1472,1893)(1473,1892)(1474,1891)(1475,1890)(1476,1889)(1477,1888)(1478,1887)(1479,1886)(1480,1885)(1481,1884)(1482,1883)(1483,1882)(1484,1881)(1485,1880)(1486,1879)(1487,1878)(1488,1877)(1489,1876)(1490,1875)(1491,1874)(1492,1873)(1493,1872)(1494,1871)(1495,1870)(1496,1869)(1497,1868)(1498,1867)(1499,1866)(1500,1865)(1501,1864)(1502,1863)(1503,1862)(1504,1861)(1505,1860)(1506,1859)(1507,1858)(1508,1857)(1509,1856)(1510,1855)(1511,1854)(1512,1853)(1513,1852)(1514,1851)(1515,1850)(1516,1849)(1517,1848)(1518,1847)(1519,1846)(1520,1845)(1521,1844)(1522,1843)(1523,1842)(1524,1841)(1525,1840)(1526,1839)(1527,1838)(1528,1837)(1529,1836)(1530,1835)(1531,1834)(1532,1833)(1533,1832)(1534,1831)(1535,1830)(1536,1829)(1537,1828)(1538,1827)(1539,1826)(1540,1825)(1541,1824)(1542,1823)(1543,1822)(1544,1821)(1545,1820)(1546,1819)(1547,1818)(1548,1817)(1549,1816)(1550,1815)(1551,1814)(1552,1813)(1553,1812)(1554,1811)(1555,1810)(1556,1809)(1557,1808)(1558,1807)(1559,1806)(1560,1805)(1561,1804)(1562,1803)(1563,1802)(1564,1801)(1565,1800)(1566,1799)(1567,1798)(1568,1797)(1569,1796)(1570,1795)(1571,1794)(1572,1793)(1573,1792)(1574,1791)(1575,1790)(1576,1789)(1577,1788)(1578,1787)(1579,1786)(1580,1785)(1581,1784)(1582,1783)(1583,1782)(1584,1781)(1585,1780)(1586,1779)(1587,1778)(1588,1777)(1589,1776)(1590,1775)(1591,1774)(1592,1773)(1593,1772)(1594,1771)(1595,1770)(1596,1769)(1597,1768)(1598,1767)(1599,1766)(1600,1765)(1601,1764)(1602,1763)(1603,1762)(1604,1761)(1605,1760)(1606,1759)(1607,1758)(1608,1757)(1609,1756)(1610,1755)(1611,1754)(1612,1753)(1613,1752)(1614,1751)(1615,1750)(1616,1749)(1617,1748)(1618,1747)(1619,1746)(1620,1745)(1621,1744)(1622,1743)(1623,1742)(1624,1741)(1625,1740)(1626,1739)(1627,1738)(1628,1737)(1629,1736)(1630,1735)(1631,1734)(1632,1733)(1633,1732)(1634,1731)(1635,1730)(1636,1729)(1637,1728)(1638,1727)(1639,1726)(1640,1725)(1641,1724)(1642,1723)(1643,1722)(1644,1721)(1645,1720)(1646,1719)(1647,1718)(1648,1717)(1649,1716)(1650,1715)(1651,1714)(1652,1713)(1653,1712)(1654,1711)(1655,1710)(1656,1709)(1657,1708)(1658,1707)(1659,1706)(1660,1705)(1661,1704)(1662,1703)(1663,1702)(1664,1701)(1665,1700)(1666,1699)(1667,1698)(1668,1697)(1669,1696)(1670,1695)(1671,1694)(1672,1693)(1673,1692)(1674,1691)(1675,1690)(1676,1689)(1677,1688)(1678,1687)(1679,1686)(1680,1685)(1681,1684)(1682,1683)

Polycyclic presentation:

2^3,3347|a^2=c,b^2=c,b^a=bc,d^b=d^3346

Conjugacy classes & character table

6697 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26776, 11);