← Prev (#34117992) Next (#34117994) →
D10083 #34117993
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3364 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);(2,3)(5,3364)(6,3363)(7,3362)(8,3361)(9,3360)(10,3359)(11,3358)(12,3357)(13,3356)(14,3355)(15,3354)(16,3353)(17,3352)(18,3351)(19,3350)(20,3349)(21,3348)(22,3347)(23,3346)(24,3345)(25,3344)(26,3343)(27,3342)(28,3341)(29,3340)(30,3339)(31,3338)(32,3337)(33,3336)(34,3335)(35,3334)(36,3333)(37,3332)(38,3331)(39,3330)(40,3329)(41,3328)(42,3327)(43,3326)(44,3325)(45,3324)(46,3323)(47,3322)(48,3321)(49,3320)(50,3319)(51,3318)(52,3317)(53,3316)(54,3315)(55,3314)(56,3313)(57,3312)(58,3311)(59,3310)(60,3309)(61,3308)(62,3307)(63,3306)(64,3305)(65,3304)(66,3303)(67,3302)(68,3301)(69,3300)(70,3299)(71,3298)(72,3297)(73,3296)(74,3295)(75,3294)(76,3293)(77,3292)(78,3291)(79,3290)(80,3289)(81,3288)(82,3287)(83,3286)(84,3285)(85,3284)(86,3283)(87,3282)(88,3281)(89,3280)(90,3279)(91,3278)(92,3277)(93,3276)(94,3275)(95,3274)(96,3273)(97,3272)(98,3271)(99,3270)(100,3269)(101,3268)(102,3267)(103,3266)(104,3265)(105,3264)(106,3263)(107,3262)(108,3261)(109,3260)(110,3259)(111,3258)(112,3257)(113,3256)(114,3255)(115,3254)(116,3253)(117,3252)(118,3251)(119,3250)(120,3249)(121,3248)(122,3247)(123,3246)(124,3245)(125,3244)(126,3243)(127,3242)(128,3241)(129,3240)(130,3239)(131,3238)(132,3237)(133,3236)(134,3235)(135,3234)(136,3233)(137,3232)(138,3231)(139,3230)(140,3229)(141,3228)(142,3227)(143,3226)(144,3225)(145,3224)(146,3223)(147,3222)(148,3221)(149,3220)(150,3219)(151,3218)(152,3217)(153,3216)(154,3215)(155,3214)(156,3213)(157,3212)(158,3211)(159,3210)(160,3209)(161,3208)(162,3207)(163,3206)(164,3205)(165,3204)(166,3203)(167,3202)(168,3201)(169,3200)(170,3199)(171,3198)(172,3197)(173,3196)(174,3195)(175,3194)(176,3193)(177,3192)(178,3191)(179,3190)(180,3189)(181,3188)(182,3187)(183,3186)(184,3185)(185,3184)(186,3183)(187,3182)(188,3181)(189,3180)(190,3179)(191,3178)(192,3177)(193,3176)(194,3175)(195,3174)(196,3173)(197,3172)(198,3171)(199,3170)(200,3169)(201,3168)(202,3167)(203,3166)(204,3165)(205,3164)(206,3163)(207,3162)(208,3161)(209,3160)(210,3159)(211,3158)(212,3157)(213,3156)(214,3155)(215,3154)(216,3153)(217,3152)(218,3151)(219,3150)(220,3149)(221,3148)(222,3147)(223,3146)(224,3145)(225,3144)(226,3143)(227,3142)(228,3141)(229,3140)(230,3139)(231,3138)(232,3137)(233,3136)(234,3135)(235,3134)(236,3133)(237,3132)(238,3131)(239,3130)(240,3129)(241,3128)(242,3127)(243,3126)(244,3125)(245,3124)(246,3123)(247,3122)(248,3121)(249,3120)(250,3119)(251,3118)(252,3117)(253,3116)(254,3115)(255,3114)(256,3113)(257,3112)(258,3111)(259,3110)(260,3109)(261,3108)(262,3107)(263,3106)(264,3105)(265,3104)(266,3103)(267,3102)(268,3101)(269,3100)(270,3099)(271,3098)(272,3097)(273,3096)(274,3095)(275,3094)(276,3093)(277,3092)(278,3091)(279,3090)(280,3089)(281,3088)(282,3087)(283,3086)(284,3085)(285,3084)(286,3083)(287,3082)(288,3081)(289,3080)(290,3079)(291,3078)(292,3077)(293,3076)(294,3075)(295,3074)(296,3073)(297,3072)(298,3071)(299,3070)(300,3069)(301,3068)(302,3067)(303,3066)(304,3065)(305,3064)(306,3063)(307,3062)(308,3061)(309,3060)(310,3059)(311,3058)(312,3057)(313,3056)(314,3055)(315,3054)(316,3053)(317,3052)(318,3051)(319,3050)(320,3049)(321,3048)(322,3047)(323,3046)(324,3045)(325,3044)(326,3043)(327,3042)(328,3041)(329,3040)(330,3039)(331,3038)(332,3037)(333,3036)(334,3035)(335,3034)(336,3033)(337,3032)(338,3031)(339,3030)(340,3029)(341,3028)(342,3027)(343,3026)(344,3025)(345,3024)(346,3023)(347,3022)(348,3021)(349,3020)(350,3019)(351,3018)(352,3017)(353,3016)(354,3015)(355,3014)(356,3013)(357,3012)(358,3011)(359,3010)(360,3009)(361,3008)(362,3007)(363,3006)(364,3005)(365,3004)(366,3003)(367,3002)(368,3001)(369,3000)(370,2999)(371,2998)(372,2997)(373,2996)(374,2995)(375,2994)(376,2993)(377,2992)(378,2991)(379,2990)(380,2989)(381,2988)(382,2987)(383,2986)(384,2985)(385,2984)(386,2983)(387,2982)(388,2981)(389,2980)(390,2979)(391,2978)(392,2977)(393,2976)(394,2975)(395,2974)(396,2973)(397,2972)(398,2971)(399,2970)(400,2969)(401,2968)(402,2967)(403,2966)(404,2965)(405,2964)(406,2963)(407,2962)(408,2961)(409,2960)(410,2959)(411,2958)(412,2957)(413,2956)(414,2955)(415,2954)(416,2953)(417,2952)(418,2951)(419,2950)(420,2949)(421,2948)(422,2947)(423,2946)(424,2945)(425,2944)(426,2943)(427,2942)(428,2941)(429,2940)(430,2939)(431,2938)(432,2937)(433,2936)(434,2935)(435,2934)(436,2933)(437,2932)(438,2931)(439,2930)(440,2929)(441,2928)(442,2927)(443,2926)(444,2925)(445,2924)(446,2923)(447,2922)(448,2921)(449,2920)(450,2919)(451,2918)(452,2917)(453,2916)(454,2915)(455,2914)(456,2913)(457,2912)(458,2911)(459,2910)(460,2909)(461,2908)(462,2907)(463,2906)(464,2905)(465,2904)(466,2903)(467,2902)(468,2901)(469,2900)(470,2899)(471,2898)(472,2897)(473,2896)(474,2895)(475,2894)(476,2893)(477,2892)(478,2891)(479,2890)(480,2889)(481,2888)(482,2887)(483,2886)(484,2885)(485,2884)(486,2883)(487,2882)(488,2881)(489,2880)(490,2879)(491,2878)(492,2877)(493,2876)(494,2875)(495,2874)(496,2873)(497,2872)(498,2871)(499,2870)(500,2869)(501,2868)(502,2867)(503,2866)(504,2865)(505,2864)(506,2863)(507,2862)(508,2861)(509,2860)(510,2859)(511,2858)(512,2857)(513,2856)(514,2855)(515,2854)(516,2853)(517,2852)(518,2851)(519,2850)(520,2849)(521,2848)(522,2847)(523,2846)(524,2845)(525,2844)(526,2843)(527,2842)(528,2841)(529,2840)(530,2839)(531,2838)(532,2837)(533,2836)(534,2835)(535,2834)(536,2833)(537,2832)(538,2831)(539,2830)(540,2829)(541,2828)(542,2827)(543,2826)(544,2825)(545,2824)(546,2823)(547,2822)(548,2821)(549,2820)(550,2819)(551,2818)(552,2817)(553,2816)(554,2815)(555,2814)(556,2813)(557,2812)(558,2811)(559,2810)(560,2809)(561,2808)(562,2807)(563,2806)(564,2805)(565,2804)(566,2803)(567,2802)(568,2801)(569,2800)(570,2799)(571,2798)(572,2797)(573,2796)(574,2795)(575,2794)(576,2793)(577,2792)(578,2791)(579,2790)(580,2789)(581,2788)(582,2787)(583,2786)(584,2785)(585,2784)(586,2783)(587,2782)(588,2781)(589,2780)(590,2779)(591,2778)(592,2777)(593,2776)(594,2775)(595,2774)(596,2773)(597,2772)(598,2771)(599,2770)(600,2769)(601,2768)(602,2767)(603,2766)(604,2765)(605,2764)(606,2763)(607,2762)(608,2761)(609,2760)(610,2759)(611,2758)(612,2757)(613,2756)(614,2755)(615,2754)(616,2753)(617,2752)(618,2751)(619,2750)(620,2749)(621,2748)(622,2747)(623,2746)(624,2745)(625,2744)(626,2743)(627,2742)(628,2741)(629,2740)(630,2739)(631,2738)(632,2737)(633,2736)(634,2735)(635,2734)(636,2733)(637,2732)(638,2731)(639,2730)(640,2729)(641,2728)(642,2727)(643,2726)(644,2725)(645,2724)(646,2723)(647,2722)(648,2721)(649,2720)(650,2719)(651,2718)(652,2717)(653,2716)(654,2715)(655,2714)(656,2713)(657,2712)(658,2711)(659,2710)(660,2709)(661,2708)(662,2707)(663,2706)(664,2705)(665,2704)(666,2703)(667,2702)(668,2701)(669,2700)(670,2699)(671,2698)(672,2697)(673,2696)(674,2695)(675,2694)(676,2693)(677,2692)(678,2691)(679,2690)(680,2689)(681,2688)(682,2687)(683,2686)(684,2685)(685,2684)(686,2683)(687,2682)(688,2681)(689,2680)(690,2679)(691,2678)(692,2677)(693,2676)(694,2675)(695,2674)(696,2673)(697,2672)(698,2671)(699,2670)(700,2669)(701,2668)(702,2667)(703,2666)(704,2665)(705,2664)(706,2663)(707,2662)(708,2661)(709,2660)(710,2659)(711,2658)(712,2657)(713,2656)(714,2655)(715,2654)(716,2653)(717,2652)(718,2651)(719,2650)(720,2649)(721,2648)(722,2647)(723,2646)(724,2645)(725,2644)(726,2643)(727,2642)(728,2641)(729,2640)(730,2639)(731,2638)(732,2637)(733,2636)(734,2635)(735,2634)(736,2633)(737,2632)(738,2631)(739,2630)(740,2629)(741,2628)(742,2627)(743,2626)(744,2625)(745,2624)(746,2623)(747,2622)(748,2621)(749,2620)(750,2619)(751,2618)(752,2617)(753,2616)(754,2615)(755,2614)(756,2613)(757,2612)(758,2611)(759,2610)(760,2609)(761,2608)(762,2607)(763,2606)(764,2605)(765,2604)(766,2603)(767,2602)(768,2601)(769,2600)(770,2599)(771,2598)(772,2597)(773,2596)(774,2595)(775,2594)(776,2593)(777,2592)(778,2591)(779,2590)(780,2589)(781,2588)(782,2587)(783,2586)(784,2585)(785,2584)(786,2583)(787,2582)(788,2581)(789,2580)(790,2579)(791,2578)(792,2577)(793,2576)(794,2575)(795,2574)(796,2573)(797,2572)(798,2571)(799,2570)(800,2569)(801,2568)(802,2567)(803,2566)(804,2565)(805,2564)(806,2563)(807,2562)(808,2561)(809,2560)(810,2559)(811,2558)(812,2557)(813,2556)(814,2555)(815,2554)(816,2553)(817,2552)(818,2551)(819,2550)(820,2549)(821,2548)(822,2547)(823,2546)(824,2545)(825,2544)(826,2543)(827,2542)(828,2541)(829,2540)(830,2539)(831,2538)(832,2537)(833,2536)(834,2535)(835,2534)(836,2533)(837,2532)(838,2531)(839,2530)(840,2529)(841,2528)(842,2527)(843,2526)(844,2525)(845,2524)(846,2523)(847,2522)(848,2521)(849,2520)(850,2519)(851,2518)(852,2517)(853,2516)(854,2515)(855,2514)(856,2513)(857,2512)(858,2511)(859,2510)(860,2509)(861,2508)(862,2507)(863,2506)(864,2505)(865,2504)(866,2503)(867,2502)(868,2501)(869,2500)(870,2499)(871,2498)(872,2497)(873,2496)(874,2495)(875,2494)(876,2493)(877,2492)(878,2491)(879,2490)(880,2489)(881,2488)(882,2487)(883,2486)(884,2485)(885,2484)(886,2483)(887,2482)(888,2481)(889,2480)(890,2479)(891,2478)(892,2477)(893,2476)(894,2475)(895,2474)(896,2473)(897,2472)(898,2471)(899,2470)(900,2469)(901,2468)(902,2467)(903,2466)(904,2465)(905,2464)(906,2463)(907,2462)(908,2461)(909,2460)(910,2459)(911,2458)(912,2457)(913,2456)(914,2455)(915,2454)(916,2453)(917,2452)(918,2451)(919,2450)(920,2449)(921,2448)(922,2447)(923,2446)(924,2445)(925,2444)(926,2443)(927,2442)(928,2441)(929,2440)(930,2439)(931,2438)(932,2437)(933,2436)(934,2435)(935,2434)(936,2433)(937,2432)(938,2431)(939,2430)(940,2429)(941,2428)(942,2427)(943,2426)(944,2425)(945,2424)(946,2423)(947,2422)(948,2421)(949,2420)(950,2419)(951,2418)(952,2417)(953,2416)(954,2415)(955,2414)(956,2413)(957,2412)(958,2411)(959,2410)(960,2409)(961,2408)(962,2407)(963,2406)(964,2405)(965,2404)(966,2403)(967,2402)(968,2401)(969,2400)(970,2399)(971,2398)(972,2397)(973,2396)(974,2395)(975,2394)(976,2393)(977,2392)(978,2391)(979,2390)(980,2389)(981,2388)(982,2387)(983,2386)(984,2385)(985,2384)(986,2383)(987,2382)(988,2381)(989,2380)(990,2379)(991,2378)(992,2377)(993,2376)(994,2375)(995,2374)(996,2373)(997,2372)(998,2371)(999,2370)(1000,2369)(1001,2368)(1002,2367)(1003,2366)(1004,2365)(1005,2364)(1006,2363)(1007,2362)(1008,2361)(1009,2360)(1010,2359)(1011,2358)(1012,2357)(1013,2356)(1014,2355)(1015,2354)(1016,2353)(1017,2352)(1018,2351)(1019,2350)(1020,2349)(1021,2348)(1022,2347)(1023,2346)(1024,2345)(1025,2344)(1026,2343)(1027,2342)(1028,2341)(1029,2340)(1030,2339)(1031,2338)(1032,2337)(1033,2336)(1034,2335)(1035,2334)(1036,2333)(1037,2332)(1038,2331)(1039,2330)(1040,2329)(1041,2328)(1042,2327)(1043,2326)(1044,2325)(1045,2324)(1046,2323)(1047,2322)(1048,2321)(1049,2320)(1050,2319)(1051,2318)(1052,2317)(1053,2316)(1054,2315)(1055,2314)(1056,2313)(1057,2312)(1058,2311)(1059,2310)(1060,2309)(1061,2308)(1062,2307)(1063,2306)(1064,2305)(1065,2304)(1066,2303)(1067,2302)(1068,2301)(1069,2300)(1070,2299)(1071,2298)(1072,2297)(1073,2296)(1074,2295)(1075,2294)(1076,2293)(1077,2292)(1078,2291)(1079,2290)(1080,2289)(1081,2288)(1082,2287)(1083,2286)(1084,2285)(1085,2284)(1086,2283)(1087,2282)(1088,2281)(1089,2280)(1090,2279)(1091,2278)(1092,2277)(1093,2276)(1094,2275)(1095,2274)(1096,2273)(1097,2272)(1098,2271)(1099,2270)(1100,2269)(1101,2268)(1102,2267)(1103,2266)(1104,2265)(1105,2264)(1106,2263)(1107,2262)(1108,2261)(1109,2260)(1110,2259)(1111,2258)(1112,2257)(1113,2256)(1114,2255)(1115,2254)(1116,2253)(1117,2252)(1118,2251)(1119,2250)(1120,2249)(1121,2248)(1122,2247)(1123,2246)(1124,2245)(1125,2244)(1126,2243)(1127,2242)(1128,2241)(1129,2240)(1130,2239)(1131,2238)(1132,2237)(1133,2236)(1134,2235)(1135,2234)(1136,2233)(1137,2232)(1138,2231)(1139,2230)(1140,2229)(1141,2228)(1142,2227)(1143,2226)(1144,2225)(1145,2224)(1146,2223)(1147,2222)(1148,2221)(1149,2220)(1150,2219)(1151,2218)(1152,2217)(1153,2216)(1154,2215)(1155,2214)(1156,2213)(1157,2212)(1158,2211)(1159,2210)(1160,2209)(1161,2208)(1162,2207)(1163,2206)(1164,2205)(1165,2204)(1166,2203)(1167,2202)(1168,2201)(1169,2200)(1170,2199)(1171,2198)(1172,2197)(1173,2196)(1174,2195)(1175,2194)(1176,2193)(1177,2192)(1178,2191)(1179,2190)(1180,2189)(1181,2188)(1182,2187)(1183,2186)(1184,2185)(1185,2184)(1186,2183)(1187,2182)(1188,2181)(1189,2180)(1190,2179)(1191,2178)(1192,2177)(1193,2176)(1194,2175)(1195,2174)(1196,2173)(1197,2172)(1198,2171)(1199,2170)(1200,2169)(1201,2168)(1202,2167)(1203,2166)(1204,2165)(1205,2164)(1206,2163)(1207,2162)(1208,2161)(1209,2160)(1210,2159)(1211,2158)(1212,2157)(1213,2156)(1214,2155)(1215,2154)(1216,2153)(1217,2152)(1218,2151)(1219,2150)(1220,2149)(1221,2148)(1222,2147)(1223,2146)(1224,2145)(1225,2144)(1226,2143)(1227,2142)(1228,2141)(1229,2140)(1230,2139)(1231,2138)(1232,2137)(1233,2136)(1234,2135)(1235,2134)(1236,2133)(1237,2132)(1238,2131)(1239,2130)(1240,2129)(1241,2128)(1242,2127)(1243,2126)(1244,2125)(1245,2124)(1246,2123)(1247,2122)(1248,2121)(1249,2120)(1250,2119)(1251,2118)(1252,2117)(1253,2116)(1254,2115)(1255,2114)(1256,2113)(1257,2112)(1258,2111)(1259,2110)(1260,2109)(1261,2108)(1262,2107)(1263,2106)(1264,2105)(1265,2104)(1266,2103)(1267,2102)(1268,2101)(1269,2100)(1270,2099)(1271,2098)(1272,2097)(1273,2096)(1274,2095)(1275,2094)(1276,2093)(1277,2092)(1278,2091)(1279,2090)(1280,2089)(1281,2088)(1282,2087)(1283,2086)(1284,2085)(1285,2084)(1286,2083)(1287,2082)(1288,2081)(1289,2080)(1290,2079)(1291,2078)(1292,2077)(1293,2076)(1294,2075)(1295,2074)(1296,2073)(1297,2072)(1298,2071)(1299,2070)(1300,2069)(1301,2068)(1302,2067)(1303,2066)(1304,2065)(1305,2064)(1306,2063)(1307,2062)(1308,2061)(1309,2060)(1310,2059)(1311,2058)(1312,2057)(1313,2056)(1314,2055)(1315,2054)(1316,2053)(1317,2052)(1318,2051)(1319,2050)(1320,2049)(1321,2048)(1322,2047)(1323,2046)(1324,2045)(1325,2044)(1326,2043)(1327,2042)(1328,2041)(1329,2040)(1330,2039)(1331,2038)(1332,2037)(1333,2036)(1334,2035)(1335,2034)(1336,2033)(1337,2032)(1338,2031)(1339,2030)(1340,2029)(1341,2028)(1342,2027)(1343,2026)(1344,2025)(1345,2024)(1346,2023)(1347,2022)(1348,2021)(1349,2020)(1350,2019)(1351,2018)(1352,2017)(1353,2016)(1354,2015)(1355,2014)(1356,2013)(1357,2012)(1358,2011)(1359,2010)(1360,2009)(1361,2008)(1362,2007)(1363,2006)(1364,2005)(1365,2004)(1366,2003)(1367,2002)(1368,2001)(1369,2000)(1370,1999)(1371,1998)(1372,1997)(1373,1996)(1374,1995)(1375,1994)(1376,1993)(1377,1992)(1378,1991)(1379,1990)(1380,1989)(1381,1988)(1382,1987)(1383,1986)(1384,1985)(1385,1984)(1386,1983)(1387,1982)(1388,1981)(1389,1980)(1390,1979)(1391,1978)(1392,1977)(1393,1976)(1394,1975)(1395,1974)(1396,1973)(1397,1972)(1398,1971)(1399,1970)(1400,1969)(1401,1968)(1402,1967)(1403,1966)(1404,1965)(1405,1964)(1406,1963)(1407,1962)(1408,1961)(1409,1960)(1410,1959)(1411,1958)(1412,1957)(1413,1956)(1414,1955)(1415,1954)(1416,1953)(1417,1952)(1418,1951)(1419,1950)(1420,1949)(1421,1948)(1422,1947)(1423,1946)(1424,1945)(1425,1944)(1426,1943)(1427,1942)(1428,1941)(1429,1940)(1430,1939)(1431,1938)(1432,1937)(1433,1936)(1434,1935)(1435,1934)(1436,1933)(1437,1932)(1438,1931)(1439,1930)(1440,1929)(1441,1928)(1442,1927)(1443,1926)(1444,1925)(1445,1924)(1446,1923)(1447,1922)(1448,1921)(1449,1920)(1450,1919)(1451,1918)(1452,1917)(1453,1916)(1454,1915)(1455,1914)(1456,1913)(1457,1912)(1458,1911)(1459,1910)(1460,1909)(1461,1908)(1462,1907)(1463,1906)(1464,1905)(1465,1904)(1466,1903)(1467,1902)(1468,1901)(1469,1900)(1470,1899)(1471,1898)(1472,1897)(1473,1896)(1474,1895)(1475,1894)(1476,1893)(1477,1892)(1478,1891)(1479,1890)(1480,1889)(1481,1888)(1482,1887)(1483,1886)(1484,1885)(1485,1884)(1486,1883)(1487,1882)(1488,1881)(1489,1880)(1490,1879)(1491,1878)(1492,1877)(1493,1876)(1494,1875)(1495,1874)(1496,1873)(1497,1872)(1498,1871)(1499,1870)(1500,1869)(1501,1868)(1502,1867)(1503,1866)(1504,1865)(1505,1864)(1506,1863)(1507,1862)(1508,1861)(1509,1860)(1510,1859)(1511,1858)(1512,1857)(1513,1856)(1514,1855)(1515,1854)(1516,1853)(1517,1852)(1518,1851)(1519,1850)(1520,1849)(1521,1848)(1522,1847)(1523,1846)(1524,1845)(1525,1844)(1526,1843)(1527,1842)(1528,1841)(1529,1840)(1530,1839)(1531,1838)(1532,1837)(1533,1836)(1534,1835)(1535,1834)(1536,1833)(1537,1832)(1538,1831)(1539,1830)(1540,1829)(1541,1828)(1542,1827)(1543,1826)(1544,1825)(1545,1824)(1546,1823)(1547,1822)(1548,1821)(1549,1820)(1550,1819)(1551,1818)(1552,1817)(1553,1816)(1554,1815)(1555,1814)(1556,1813)(1557,1812)(1558,1811)(1559,1810)(1560,1809)(1561,1808)(1562,1807)(1563,1806)(1564,1805)(1565,1804)(1566,1803)(1567,1802)(1568,1801)(1569,1800)(1570,1799)(1571,1798)(1572,1797)(1573,1796)(1574,1795)(1575,1794)(1576,1793)(1577,1792)(1578,1791)(1579,1790)(1580,1789)(1581,1788)(1582,1787)(1583,1786)(1584,1785)(1585,1784)(1586,1783)(1587,1782)(1588,1781)(1589,1780)(1590,1779)(1591,1778)(1592,1777)(1593,1776)(1594,1775)(1595,1774)(1596,1773)(1597,1772)(1598,1771)(1599,1770)(1600,1769)(1601,1768)(1602,1767)(1603,1766)(1604,1765)(1605,1764)(1606,1763)(1607,1762)(1608,1761)(1609,1760)(1610,1759)(1611,1758)(1612,1757)(1613,1756)(1614,1755)(1615,1754)(1616,1753)(1617,1752)(1618,1751)(1619,1750)(1620,1749)(1621,1748)(1622,1747)(1623,1746)(1624,1745)(1625,1744)(1626,1743)(1627,1742)(1628,1741)(1629,1740)(1630,1739)(1631,1738)(1632,1737)(1633,1736)(1634,1735)(1635,1734)(1636,1733)(1637,1732)(1638,1731)(1639,1730)(1640,1729)(1641,1728)(1642,1727)(1643,1726)(1644,1725)(1645,1724)(1646,1723)(1647,1722)(1648,1721)(1649,1720)(1650,1719)(1651,1718)(1652,1717)(1653,1716)(1654,1715)(1655,1714)(1656,1713)(1657,1712)(1658,1711)(1659,1710)(1660,1709)(1661,1708)(1662,1707)(1663,1706)(1664,1705)(1665,1704)(1666,1703)(1667,1702)(1668,1701)(1669,1700)(1670,1699)(1671,1698)(1672,1697)(1673,1696)(1674,1695)(1675,1694)(1676,1693)(1677,1692)(1678,1691)(1679,1690)(1680,1689)(1681,1688)(1682,1687)(1683,1686)(1684,1685)
Polycyclic presentation:
2,3,3361|b^a=b^2,c^a=c^3360
Conjugacy classes & character table
5043 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20166, 5);
Finite Group Databasebeta