Finite Group Databasebeta

?

← Prev (#72295967) Next (#72295969) →

D₃₀₆₆₃ #72295968

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

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 3416 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,2721,2722,2723,2724,2725,2726,2727,2728,2729,2730,2731,2732,2733,2734,2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,2751,2752,2753,2754,2755,2756,2757,2758,2759,2760,2761,2762,2763,2764,2765,2766,2767,2768,2769,2770,2771,2772,2773,2774,2775,2776,2777,2778,2779,2780,2781,2782,2783,2784,2785,2786,2787,2788,2789,2790,2791,2792,2793,2794,2795,2796,2797,2798,2799,2800,2801,2802,2803,2804,2805,2806,2807,2808,2809,2810,2811,2812,2813,2814,2815,2816,2817,2818,2819,2820,2821,2822,2823,2824,2825,2826,2827,2828,2829,2830,2831,2832,2833,2834,2835,2836,2837,2838,2839,2840,2841,2842,2843,2844,2845,2846,2847,2848,2849,2850,2851,2852,2853,2854,2855,2856,2857,2858,2859,2860,2861,2862,2863,2864,2865,2866,2867,2868,2869,2870,2871,2872,2873,2874,2875,2876,2877,2878,2879,2880,2881,2882,2883,2884,2885,2886,2887,2888,2889,2890,2891,2892,2893,2894,2895,2896,2897,2898,2899,2900,2901,2902,2903,2904,2905,2906,2907,2908,2909,2910,2911,2912,2913,2914,2915,2916,2917,2918,2919,2920,2921,2922,2923,2924,2925,2926,2927,2928,2929,2930,2931,2932,2933,2934,2935,2936,2937,2938,2939,2940,2941,2942,2943,2944,2945,2946,2947,2948,2949,2950,2951,2952,2953,2954,2955,2956,2957,2958,2959,2960,2961,2962,2963,2964,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,2977,2978,2979,2980,2981,2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003,3004,3005,3006,3007,3008,3009,3010,3011,3012,3013,3014,3015,3016,3017,3018,3019,3020,3021,3022,3023,3024,3025,3026,3027,3028,3029,3030,3031,3032,3033,3034,3035,3036,3037,3038,3039,3040,3041,3042,3043,3044,3045,3046,3047,3048,3049,3050,3051,3052,3053,3054,3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,3067,3068,3069,3070,3071,3072,3073,3074,3075,3076,3077,3078,3079,3080,3081,3082,3083,3084,3085,3086,3087,3088,3089,3090,3091,3092,3093,3094,3095,3096,3097,3098,3099,3100,3101,3102,3103,3104,3105,3106,3107,3108,3109,3110,3111,3112,3113,3114,3115,3116,3117,3118,3119,3120,3121,3122,3123,3124,3125,3126,3127,3128,3129,3130,3131,3132,3133,3134,3135,3136,3137,3138,3139,3140,3141,3142,3143,3144,3145,3146,3147,3148,3149,3150,3151,3152,3153,3154,3155,3156,3157,3158,3159,3160,3161,3162,3163,3164,3165,3166,3167,3168,3169,3170,3171,3172,3173,3174,3175,3176,3177,3178,3179,3180,3181,3182,3183,3184,3185,3186,3187,3188,3189,3190,3191,3192,3193,3194,3195,3196,3197,3198,3199,3200,3201,3202,3203,3204,3205,3206,3207,3208,3209,3210,3211,3212,3213,3214,3215,3216,3217,3218,3219,3220,3221,3222,3223,3224,3225,3226,3227,3228,3229,3230,3231,3232,3233,3234,3235,3236,3237,3238,3239,3240,3241,3242,3243,3244,3245,3246,3247,3248,3249,3250,3251,3252,3253,3254,3255,3256,3257,3258,3259,3260,3261,3262,3263,3264,3265,3266,3267,3268,3269,3270,3271,3272,3273,3274,3275,3276,3277,3278,3279,3280,3281,3282,3283,3284,3285,3286,3287,3288,3289,3290,3291,3292,3293,3294,3295,3296,3297,3298,3299,3300,3301,3302,3303,3304,3305,3306,3307,3308,3309,3310,3311,3312,3313,3314,3315,3316,3317,3318,3319,3320,3321,3322,3323,3324,3325,3326,3327,3328,3329,3330,3331,3332,3333,3334,3335,3336,3337,3338,3339,3340,3341,3342,3343,3344,3345,3346,3347,3348,3349,3350,3351,3352,3353,3354,3355,3356,3357,3358,3359,3360,3361,3362,3363,3364,3365,3366,3367,3368,3369,3370,3371,3372,3373,3374,3375,3376,3377,3378,3379,3380,3381,3382,3383,3384,3385,3386,3387,3388,3389,3390,3391,3392,3393,3394,3395,3396,3397,3398,3399,3400,3401,3402,3403,3404,3405,3406,3407,3408,3409,3410,3411,3412,3413,3414,3415,3416);(2,9)(3,8)(4,7)(5,6)(11,3416)(12,3415)(13,3414)(14,3413)(15,3412)(16,3411)(17,3410)(18,3409)(19,3408)(20,3407)(21,3406)(22,3405)(23,3404)(24,3403)(25,3402)(26,3401)(27,3400)(28,3399)(29,3398)(30,3397)(31,3396)(32,3395)(33,3394)(34,3393)(35,3392)(36,3391)(37,3390)(38,3389)(39,3388)(40,3387)(41,3386)(42,3385)(43,3384)(44,3383)(45,3382)(46,3381)(47,3380)(48,3379)(49,3378)(50,3377)(51,3376)(52,3375)(53,3374)(54,3373)(55,3372)(56,3371)(57,3370)(58,3369)(59,3368)(60,3367)(61,3366)(62,3365)(63,3364)(64,3363)(65,3362)(66,3361)(67,3360)(68,3359)(69,3358)(70,3357)(71,3356)(72,3355)(73,3354)(74,3353)(75,3352)(76,3351)(77,3350)(78,3349)(79,3348)(80,3347)(81,3346)(82,3345)(83,3344)(84,3343)(85,3342)(86,3341)(87,3340)(88,3339)(89,3338)(90,3337)(91,3336)(92,3335)(93,3334)(94,3333)(95,3332)(96,3331)(97,3330)(98,3329)(99,3328)(100,3327)(101,3326)(102,3325)(103,3324)(104,3323)(105,3322)(106,3321)(107,3320)(108,3319)(109,3318)(110,3317)(111,3316)(112,3315)(113,3314)(114,3313)(115,3312)(116,3311)(117,3310)(118,3309)(119,3308)(120,3307)(121,3306)(122,3305)(123,3304)(124,3303)(125,3302)(126,3301)(127,3300)(128,3299)(129,3298)(130,3297)(131,3296)(132,3295)(133,3294)(134,3293)(135,3292)(136,3291)(137,3290)(138,3289)(139,3288)(140,3287)(141,3286)(142,3285)(143,3284)(144,3283)(145,3282)(146,3281)(147,3280)(148,3279)(149,3278)(150,3277)(151,3276)(152,3275)(153,3274)(154,3273)(155,3272)(156,3271)(157,3270)(158,3269)(159,3268)(160,3267)(161,3266)(162,3265)(163,3264)(164,3263)(165,3262)(166,3261)(167,3260)(168,3259)(169,3258)(170,3257)(171,3256)(172,3255)(173,3254)(174,3253)(175,3252)(176,3251)(177,3250)(178,3249)(179,3248)(180,3247)(181,3246)(182,3245)(183,3244)(184,3243)(185,3242)(186,3241)(187,3240)(188,3239)(189,3238)(190,3237)(191,3236)(192,3235)(193,3234)(194,3233)(195,3232)(196,3231)(197,3230)(198,3229)(199,3228)(200,3227)(201,3226)(202,3225)(203,3224)(204,3223)(205,3222)(206,3221)(207,3220)(208,3219)(209,3218)(210,3217)(211,3216)(212,3215)(213,3214)(214,3213)(215,3212)(216,3211)(217,3210)(218,3209)(219,3208)(220,3207)(221,3206)(222,3205)(223,3204)(224,3203)(225,3202)(226,3201)(227,3200)(228,3199)(229,3198)(230,3197)(231,3196)(232,3195)(233,3194)(234,3193)(235,3192)(236,3191)(237,3190)(238,3189)(239,3188)(240,3187)(241,3186)(242,3185)(243,3184)(244,3183)(245,3182)(246,3181)(247,3180)(248,3179)(249,3178)(250,3177)(251,3176)(252,3175)(253,3174)(254,3173)(255,3172)(256,3171)(257,3170)(258,3169)(259,3168)(260,3167)(261,3166)(262,3165)(263,3164)(264,3163)(265,3162)(266,3161)(267,3160)(268,3159)(269,3158)(270,3157)(271,3156)(272,3155)(273,3154)(274,3153)(275,3152)(276,3151)(277,3150)(278,3149)(279,3148)(280,3147)(281,3146)(282,3145)(283,3144)(284,3143)(285,3142)(286,3141)(287,3140)(288,3139)(289,3138)(290,3137)(291,3136)(292,3135)(293,3134)(294,3133)(295,3132)(296,3131)(297,3130)(298,3129)(299,3128)(300,3127)(301,3126)(302,3125)(303,3124)(304,3123)(305,3122)(306,3121)(307,3120)(308,3119)(309,3118)(310,3117)(311,3116)(312,3115)(313,3114)(314,3113)(315,3112)(316,3111)(317,3110)(318,3109)(319,3108)(320,3107)(321,3106)(322,3105)(323,3104)(324,3103)(325,3102)(326,3101)(327,3100)(328,3099)(329,3098)(330,3097)(331,3096)(332,3095)(333,3094)(334,3093)(335,3092)(336,3091)(337,3090)(338,3089)(339,3088)(340,3087)(341,3086)(342,3085)(343,3084)(344,3083)(345,3082)(346,3081)(347,3080)(348,3079)(349,3078)(350,3077)(351,3076)(352,3075)(353,3074)(354,3073)(355,3072)(356,3071)(357,3070)(358,3069)(359,3068)(360,3067)(361,3066)(362,3065)(363,3064)(364,3063)(365,3062)(366,3061)(367,3060)(368,3059)(369,3058)(370,3057)(371,3056)(372,3055)(373,3054)(374,3053)(375,3052)(376,3051)(377,3050)(378,3049)(379,3048)(380,3047)(381,3046)(382,3045)(383,3044)(384,3043)(385,3042)(386,3041)(387,3040)(388,3039)(389,3038)(390,3037)(391,3036)(392,3035)(393,3034)(394,3033)(395,3032)(396,3031)(397,3030)(398,3029)(399,3028)(400,3027)(401,3026)(402,3025)(403,3024)(404,3023)(405,3022)(406,3021)(407,3020)(408,3019)(409,3018)(410,3017)(411,3016)(412,3015)(413,3014)(414,3013)(415,3012)(416,3011)(417,3010)(418,3009)(419,3008)(420,3007)(421,3006)(422,3005)(423,3004)(424,3003)(425,3002)(426,3001)(427,3000)(428,2999)(429,2998)(430,2997)(431,2996)(432,2995)(433,2994)(434,2993)(435,2992)(436,2991)(437,2990)(438,2989)(439,2988)(440,2987)(441,2986)(442,2985)(443,2984)(444,2983)(445,2982)(446,2981)(447,2980)(448,2979)(449,2978)(450,2977)(451,2976)(452,2975)(453,2974)(454,2973)(455,2972)(456,2971)(457,2970)(458,2969)(459,2968)(460,2967)(461,2966)(462,2965)(463,2964)(464,2963)(465,2962)(466,2961)(467,2960)(468,2959)(469,2958)(470,2957)(471,2956)(472,2955)(473,2954)(474,2953)(475,2952)(476,2951)(477,2950)(478,2949)(479,2948)(480,2947)(481,2946)(482,2945)(483,2944)(484,2943)(485,2942)(486,2941)(487,2940)(488,2939)(489,2938)(490,2937)(491,2936)(492,2935)(493,2934)(494,2933)(495,2932)(496,2931)(497,2930)(498,2929)(499,2928)(500,2927)(501,2926)(502,2925)(503,2924)(504,2923)(505,2922)(506,2921)(507,2920)(508,2919)(509,2918)(510,2917)(511,2916)(512,2915)(513,2914)(514,2913)(515,2912)(516,2911)(517,2910)(518,2909)(519,2908)(520,2907)(521,2906)(522,2905)(523,2904)(524,2903)(525,2902)(526,2901)(527,2900)(528,2899)(529,2898)(530,2897)(531,2896)(532,2895)(533,2894)(534,2893)(535,2892)(536,2891)(537,2890)(538,2889)(539,2888)(540,2887)(541,2886)(542,2885)(543,2884)(544,2883)(545,2882)(546,2881)(547,2880)(548,2879)(549,2878)(550,2877)(551,2876)(552,2875)(553,2874)(554,2873)(555,2872)(556,2871)(557,2870)(558,2869)(559,2868)(560,2867)(561,2866)(562,2865)(563,2864)(564,2863)(565,2862)(566,2861)(567,2860)(568,2859)(569,2858)(570,2857)(571,2856)(572,2855)(573,2854)(574,2853)(575,2852)(576,2851)(577,2850)(578,2849)(579,2848)(580,2847)(581,2846)(582,2845)(583,2844)(584,2843)(585,2842)(586,2841)(587,2840)(588,2839)(589,2838)(590,2837)(591,2836)(592,2835)(593,2834)(594,2833)(595,2832)(596,2831)(597,2830)(598,2829)(599,2828)(600,2827)(601,2826)(602,2825)(603,2824)(604,2823)(605,2822)(606,2821)(607,2820)(608,2819)(609,2818)(610,2817)(611,2816)(612,2815)(613,2814)(614,2813)(615,2812)(616,2811)(617,2810)(618,2809)(619,2808)(620,2807)(621,2806)(622,2805)(623,2804)(624,2803)(625,2802)(626,2801)(627,2800)(628,2799)(629,2798)(630,2797)(631,2796)(632,2795)(633,2794)(634,2793)(635,2792)(636,2791)(637,2790)(638,2789)(639,2788)(640,2787)(641,2786)(642,2785)(643,2784)(644,2783)(645,2782)(646,2781)(647,2780)(648,2779)(649,2778)(650,2777)(651,2776)(652,2775)(653,2774)(654,2773)(655,2772)(656,2771)(657,2770)(658,2769)(659,2768)(660,2767)(661,2766)(662,2765)(663,2764)(664,2763)(665,2762)(666,2761)(667,2760)(668,2759)(669,2758)(670,2757)(671,2756)(672,2755)(673,2754)(674,2753)(675,2752)(676,2751)(677,2750)(678,2749)(679,2748)(680,2747)(681,2746)(682,2745)(683,2744)(684,2743)(685,2742)(686,2741)(687,2740)(688,2739)(689,2738)(690,2737)(691,2736)(692,2735)(693,2734)(694,2733)(695,2732)(696,2731)(697,2730)(698,2729)(699,2728)(700,2727)(701,2726)(702,2725)(703,2724)(704,2723)(705,2722)(706,2721)(707,2720)(708,2719)(709,2718)(710,2717)(711,2716)(712,2715)(713,2714)(714,2713)(715,2712)(716,2711)(717,2710)(718,2709)(719,2708)(720,2707)(721,2706)(722,2705)(723,2704)(724,2703)(725,2702)(726,2701)(727,2700)(728,2699)(729,2698)(730,2697)(731,2696)(732,2695)(733,2694)(734,2693)(735,2692)(736,2691)(737,2690)(738,2689)(739,2688)(740,2687)(741,2686)(742,2685)(743,2684)(744,2683)(745,2682)(746,2681)(747,2680)(748,2679)(749,2678)(750,2677)(751,2676)(752,2675)(753,2674)(754,2673)(755,2672)(756,2671)(757,2670)(758,2669)(759,2668)(760,2667)(761,2666)(762,2665)(763,2664)(764,2663)(765,2662)(766,2661)(767,2660)(768,2659)(769,2658)(770,2657)(771,2656)(772,2655)(773,2654)(774,2653)(775,2652)(776,2651)(777,2650)(778,2649)(779,2648)(780,2647)(781,2646)(782,2645)(783,2644)(784,2643)(785,2642)(786,2641)(787,2640)(788,2639)(789,2638)(790,2637)(791,2636)(792,2635)(793,2634)(794,2633)(795,2632)(796,2631)(797,2630)(798,2629)(799,2628)(800,2627)(801,2626)(802,2625)(803,2624)(804,2623)(805,2622)(806,2621)(807,2620)(808,2619)(809,2618)(810,2617)(811,2616)(812,2615)(813,2614)(814,2613)(815,2612)(816,2611)(817,2610)(818,2609)(819,2608)(820,2607)(821,2606)(822,2605)(823,2604)(824,2603)(825,2602)(826,2601)(827,2600)(828,2599)(829,2598)(830,2597)(831,2596)(832,2595)(833,2594)(834,2593)(835,2592)(836,2591)(837,2590)(838,2589)(839,2588)(840,2587)(841,2586)(842,2585)(843,2584)(844,2583)(845,2582)(846,2581)(847,2580)(848,2579)(849,2578)(850,2577)(851,2576)(852,2575)(853,2574)(854,2573)(855,2572)(856,2571)(857,2570)(858,2569)(859,2568)(860,2567)(861,2566)(862,2565)(863,2564)(864,2563)(865,2562)(866,2561)(867,2560)(868,2559)(869,2558)(870,2557)(871,2556)(872,2555)(873,2554)(874,2553)(875,2552)(876,2551)(877,2550)(878,2549)(879,2548)(880,2547)(881,2546)(882,2545)(883,2544)(884,2543)(885,2542)(886,2541)(887,2540)(888,2539)(889,2538)(890,2537)(891,2536)(892,2535)(893,2534)(894,2533)(895,2532)(896,2531)(897,2530)(898,2529)(899,2528)(900,2527)(901,2526)(902,2525)(903,2524)(904,2523)(905,2522)(906,2521)(907,2520)(908,2519)(909,2518)(910,2517)(911,2516)(912,2515)(913,2514)(914,2513)(915,2512)(916,2511)(917,2510)(918,2509)(919,2508)(920,2507)(921,2506)(922,2505)(923,2504)(924,2503)(925,2502)(926,2501)(927,2500)(928,2499)(929,2498)(930,2497)(931,2496)(932,2495)(933,2494)(934,2493)(935,2492)(936,2491)(937,2490)(938,2489)(939,2488)(940,2487)(941,2486)(942,2485)(943,2484)(944,2483)(945,2482)(946,2481)(947,2480)(948,2479)(949,2478)(950,2477)(951,2476)(952,2475)(953,2474)(954,2473)(955,2472)(956,2471)(957,2470)(958,2469)(959,2468)(960,2467)(961,2466)(962,2465)(963,2464)(964,2463)(965,2462)(966,2461)(967,2460)(968,2459)(969,2458)(970,2457)(971,2456)(972,2455)(973,2454)(974,2453)(975,2452)(976,2451)(977,2450)(978,2449)(979,2448)(980,2447)(981,2446)(982,2445)(983,2444)(984,2443)(985,2442)(986,2441)(987,2440)(988,2439)(989,2438)(990,2437)(991,2436)(992,2435)(993,2434)(994,2433)(995,2432)(996,2431)(997,2430)(998,2429)(999,2428)(1000,2427)(1001,2426)(1002,2425)(1003,2424)(1004,2423)(1005,2422)(1006,2421)(1007,2420)(1008,2419)(1009,2418)(1010,2417)(1011,2416)(1012,2415)(1013,2414)(1014,2413)(1015,2412)(1016,2411)(1017,2410)(1018,2409)(1019,2408)(1020,2407)(1021,2406)(1022,2405)(1023,2404)(1024,2403)(1025,2402)(1026,2401)(1027,2400)(1028,2399)(1029,2398)(1030,2397)(1031,2396)(1032,2395)(1033,2394)(1034,2393)(1035,2392)(1036,2391)(1037,2390)(1038,2389)(1039,2388)(1040,2387)(1041,2386)(1042,2385)(1043,2384)(1044,2383)(1045,2382)(1046,2381)(1047,2380)(1048,2379)(1049,2378)(1050,2377)(1051,2376)(1052,2375)(1053,2374)(1054,2373)(1055,2372)(1056,2371)(1057,2370)(1058,2369)(1059,2368)(1060,2367)(1061,2366)(1062,2365)(1063,2364)(1064,2363)(1065,2362)(1066,2361)(1067,2360)(1068,2359)(1069,2358)(1070,2357)(1071,2356)(1072,2355)(1073,2354)(1074,2353)(1075,2352)(1076,2351)(1077,2350)(1078,2349)(1079,2348)(1080,2347)(1081,2346)(1082,2345)(1083,2344)(1084,2343)(1085,2342)(1086,2341)(1087,2340)(1088,2339)(1089,2338)(1090,2337)(1091,2336)(1092,2335)(1093,2334)(1094,2333)(1095,2332)(1096,2331)(1097,2330)(1098,2329)(1099,2328)(1100,2327)(1101,2326)(1102,2325)(1103,2324)(1104,2323)(1105,2322)(1106,2321)(1107,2320)(1108,2319)(1109,2318)(1110,2317)(1111,2316)(1112,2315)(1113,2314)(1114,2313)(1115,2312)(1116,2311)(1117,2310)(1118,2309)(1119,2308)(1120,2307)(1121,2306)(1122,2305)(1123,2304)(1124,2303)(1125,2302)(1126,2301)(1127,2300)(1128,2299)(1129,2298)(1130,2297)(1131,2296)(1132,2295)(1133,2294)(1134,2293)(1135,2292)(1136,2291)(1137,2290)(1138,2289)(1139,2288)(1140,2287)(1141,2286)(1142,2285)(1143,2284)(1144,2283)(1145,2282)(1146,2281)(1147,2280)(1148,2279)(1149,2278)(1150,2277)(1151,2276)(1152,2275)(1153,2274)(1154,2273)(1155,2272)(1156,2271)(1157,2270)(1158,2269)(1159,2268)(1160,2267)(1161,2266)(1162,2265)(1163,2264)(1164,2263)(1165,2262)(1166,2261)(1167,2260)(1168,2259)(1169,2258)(1170,2257)(1171,2256)(1172,2255)(1173,2254)(1174,2253)(1175,2252)(1176,2251)(1177,2250)(1178,2249)(1179,2248)(1180,2247)(1181,2246)(1182,2245)(1183,2244)(1184,2243)(1185,2242)(1186,2241)(1187,2240)(1188,2239)(1189,2238)(1190,2237)(1191,2236)(1192,2235)(1193,2234)(1194,2233)(1195,2232)(1196,2231)(1197,2230)(1198,2229)(1199,2228)(1200,2227)(1201,2226)(1202,2225)(1203,2224)(1204,2223)(1205,2222)(1206,2221)(1207,2220)(1208,2219)(1209,2218)(1210,2217)(1211,2216)(1212,2215)(1213,2214)(1214,2213)(1215,2212)(1216,2211)(1217,2210)(1218,2209)(1219,2208)(1220,2207)(1221,2206)(1222,2205)(1223,2204)(1224,2203)(1225,2202)(1226,2201)(1227,2200)(1228,2199)(1229,2198)(1230,2197)(1231,2196)(1232,2195)(1233,2194)(1234,2193)(1235,2192)(1236,2191)(1237,2190)(1238,2189)(1239,2188)(1240,2187)(1241,2186)(1242,2185)(1243,2184)(1244,2183)(1245,2182)(1246,2181)(1247,2180)(1248,2179)(1249,2178)(1250,2177)(1251,2176)(1252,2175)(1253,2174)(1254,2173)(1255,2172)(1256,2171)(1257,2170)(1258,2169)(1259,2168)(1260,2167)(1261,2166)(1262,2165)(1263,2164)(1264,2163)(1265,2162)(1266,2161)(1267,2160)(1268,2159)(1269,2158)(1270,2157)(1271,2156)(1272,2155)(1273,2154)(1274,2153)(1275,2152)(1276,2151)(1277,2150)(1278,2149)(1279,2148)(1280,2147)(1281,2146)(1282,2145)(1283,2144)(1284,2143)(1285,2142)(1286,2141)(1287,2140)(1288,2139)(1289,2138)(1290,2137)(1291,2136)(1292,2135)(1293,2134)(1294,2133)(1295,2132)(1296,2131)(1297,2130)(1298,2129)(1299,2128)(1300,2127)(1301,2126)(1302,2125)(1303,2124)(1304,2123)(1305,2122)(1306,2121)(1307,2120)(1308,2119)(1309,2118)(1310,2117)(1311,2116)(1312,2115)(1313,2114)(1314,2113)(1315,2112)(1316,2111)(1317,2110)(1318,2109)(1319,2108)(1320,2107)(1321,2106)(1322,2105)(1323,2104)(1324,2103)(1325,2102)(1326,2101)(1327,2100)(1328,2099)(1329,2098)(1330,2097)(1331,2096)(1332,2095)(1333,2094)(1334,2093)(1335,2092)(1336,2091)(1337,2090)(1338,2089)(1339,2088)(1340,2087)(1341,2086)(1342,2085)(1343,2084)(1344,2083)(1345,2082)(1346,2081)(1347,2080)(1348,2079)(1349,2078)(1350,2077)(1351,2076)(1352,2075)(1353,2074)(1354,2073)(1355,2072)(1356,2071)(1357,2070)(1358,2069)(1359,2068)(1360,2067)(1361,2066)(1362,2065)(1363,2064)(1364,2063)(1365,2062)(1366,2061)(1367,2060)(1368,2059)(1369,2058)(1370,2057)(1371,2056)(1372,2055)(1373,2054)(1374,2053)(1375,2052)(1376,2051)(1377,2050)(1378,2049)(1379,2048)(1380,2047)(1381,2046)(1382,2045)(1383,2044)(1384,2043)(1385,2042)(1386,2041)(1387,2040)(1388,2039)(1389,2038)(1390,2037)(1391,2036)(1392,2035)(1393,2034)(1394,2033)(1395,2032)(1396,2031)(1397,2030)(1398,2029)(1399,2028)(1400,2027)(1401,2026)(1402,2025)(1403,2024)(1404,2023)(1405,2022)(1406,2021)(1407,2020)(1408,2019)(1409,2018)(1410,2017)(1411,2016)(1412,2015)(1413,2014)(1414,2013)(1415,2012)(1416,2011)(1417,2010)(1418,2009)(1419,2008)(1420,2007)(1421,2006)(1422,2005)(1423,2004)(1424,2003)(1425,2002)(1426,2001)(1427,2000)(1428,1999)(1429,1998)(1430,1997)(1431,1996)(1432,1995)(1433,1994)(1434,1993)(1435,1992)(1436,1991)(1437,1990)(1438,1989)(1439,1988)(1440,1987)(1441,1986)(1442,1985)(1443,1984)(1444,1983)(1445,1982)(1446,1981)(1447,1980)(1448,1979)(1449,1978)(1450,1977)(1451,1976)(1452,1975)(1453,1974)(1454,1973)(1455,1972)(1456,1971)(1457,1970)(1458,1969)(1459,1968)(1460,1967)(1461,1966)(1462,1965)(1463,1964)(1464,1963)(1465,1962)(1466,1961)(1467,1960)(1468,1959)(1469,1958)(1470,1957)(1471,1956)(1472,1955)(1473,1954)(1474,1953)(1475,1952)(1476,1951)(1477,1950)(1478,1949)(1479,1948)(1480,1947)(1481,1946)(1482,1945)(1483,1944)(1484,1943)(1485,1942)(1486,1941)(1487,1940)(1488,1939)(1489,1938)(1490,1937)(1491,1936)(1492,1935)(1493,1934)(1494,1933)(1495,1932)(1496,1931)(1497,1930)(1498,1929)(1499,1928)(1500,1927)(1501,1926)(1502,1925)(1503,1924)(1504,1923)(1505,1922)(1506,1921)(1507,1920)(1508,1919)(1509,1918)(1510,1917)(1511,1916)(1512,1915)(1513,1914)(1514,1913)(1515,1912)(1516,1911)(1517,1910)(1518,1909)(1519,1908)(1520,1907)(1521,1906)(1522,1905)(1523,1904)(1524,1903)(1525,1902)(1526,1901)(1527,1900)(1528,1899)(1529,1898)(1530,1897)(1531,1896)(1532,1895)(1533,1894)(1534,1893)(1535,1892)(1536,1891)(1537,1890)(1538,1889)(1539,1888)(1540,1887)(1541,1886)(1542,1885)(1543,1884)(1544,1883)(1545,1882)(1546,1881)(1547,1880)(1548,1879)(1549,1878)(1550,1877)(1551,1876)(1552,1875)(1553,1874)(1554,1873)(1555,1872)(1556,1871)(1557,1870)(1558,1869)(1559,1868)(1560,1867)(1561,1866)(1562,1865)(1563,1864)(1564,1863)(1565,1862)(1566,1861)(1567,1860)(1568,1859)(1569,1858)(1570,1857)(1571,1856)(1572,1855)(1573,1854)(1574,1853)(1575,1852)(1576,1851)(1577,1850)(1578,1849)(1579,1848)(1580,1847)(1581,1846)(1582,1845)(1583,1844)(1584,1843)(1585,1842)(1586,1841)(1587,1840)(1588,1839)(1589,1838)(1590,1837)(1591,1836)(1592,1835)(1593,1834)(1594,1833)(1595,1832)(1596,1831)(1597,1830)(1598,1829)(1599,1828)(1600,1827)(1601,1826)(1602,1825)(1603,1824)(1604,1823)(1605,1822)(1606,1821)(1607,1820)(1608,1819)(1609,1818)(1610,1817)(1611,1816)(1612,1815)(1613,1814)(1614,1813)(1615,1812)(1616,1811)(1617,1810)(1618,1809)(1619,1808)(1620,1807)(1621,1806)(1622,1805)(1623,1804)(1624,1803)(1625,1802)(1626,1801)(1627,1800)(1628,1799)(1629,1798)(1630,1797)(1631,1796)(1632,1795)(1633,1794)(1634,1793)(1635,1792)(1636,1791)(1637,1790)(1638,1789)(1639,1788)(1640,1787)(1641,1786)(1642,1785)(1643,1784)(1644,1783)(1645,1782)(1646,1781)(1647,1780)(1648,1779)(1649,1778)(1650,1777)(1651,1776)(1652,1775)(1653,1774)(1654,1773)(1655,1772)(1656,1771)(1657,1770)(1658,1769)(1659,1768)(1660,1767)(1661,1766)(1662,1765)(1663,1764)(1664,1763)(1665,1762)(1666,1761)(1667,1760)(1668,1759)(1669,1758)(1670,1757)(1671,1756)(1672,1755)(1673,1754)(1674,1753)(1675,1752)(1676,1751)(1677,1750)(1678,1749)(1679,1748)(1680,1747)(1681,1746)(1682,1745)(1683,1744)(1684,1743)(1685,1742)(1686,1741)(1687,1740)(1688,1739)(1689,1738)(1690,1737)(1691,1736)(1692,1735)(1693,1734)(1694,1733)(1695,1732)(1696,1731)(1697,1730)(1698,1729)(1699,1728)(1700,1727)(1701,1726)(1702,1725)(1703,1724)(1704,1723)(1705,1722)(1706,1721)(1707,1720)(1708,1719)(1709,1718)(1710,1717)(1711,1716)(1712,1715)(1713,1714)

Polycyclic presentation:

2,3,3407,3|b^3=d,b^a=b^2d^2,c^a=c^3406,d^a=d^2

Conjugacy classes & character table

15333 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d");;
gap> coll := SingleCollector(F, [2, 3, 3407, 3]);;
gap> SetPower(coll, 2, F.4);;
gap> SetConjugate(coll, 2, 1, F.2^2*F.4^2);;
gap> SetConjugate(coll, 3, 1, F.3^3406);;
gap> SetConjugate(coll, 4, 1, F.4^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);