← Prev (#34095387) Next (#34095389) →
D10029 #34095388
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3346 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);(2,3)(5,3346)(6,3345)(7,3344)(8,3343)(9,3342)(10,3341)(11,3340)(12,3339)(13,3338)(14,3337)(15,3336)(16,3335)(17,3334)(18,3333)(19,3332)(20,3331)(21,3330)(22,3329)(23,3328)(24,3327)(25,3326)(26,3325)(27,3324)(28,3323)(29,3322)(30,3321)(31,3320)(32,3319)(33,3318)(34,3317)(35,3316)(36,3315)(37,3314)(38,3313)(39,3312)(40,3311)(41,3310)(42,3309)(43,3308)(44,3307)(45,3306)(46,3305)(47,3304)(48,3303)(49,3302)(50,3301)(51,3300)(52,3299)(53,3298)(54,3297)(55,3296)(56,3295)(57,3294)(58,3293)(59,3292)(60,3291)(61,3290)(62,3289)(63,3288)(64,3287)(65,3286)(66,3285)(67,3284)(68,3283)(69,3282)(70,3281)(71,3280)(72,3279)(73,3278)(74,3277)(75,3276)(76,3275)(77,3274)(78,3273)(79,3272)(80,3271)(81,3270)(82,3269)(83,3268)(84,3267)(85,3266)(86,3265)(87,3264)(88,3263)(89,3262)(90,3261)(91,3260)(92,3259)(93,3258)(94,3257)(95,3256)(96,3255)(97,3254)(98,3253)(99,3252)(100,3251)(101,3250)(102,3249)(103,3248)(104,3247)(105,3246)(106,3245)(107,3244)(108,3243)(109,3242)(110,3241)(111,3240)(112,3239)(113,3238)(114,3237)(115,3236)(116,3235)(117,3234)(118,3233)(119,3232)(120,3231)(121,3230)(122,3229)(123,3228)(124,3227)(125,3226)(126,3225)(127,3224)(128,3223)(129,3222)(130,3221)(131,3220)(132,3219)(133,3218)(134,3217)(135,3216)(136,3215)(137,3214)(138,3213)(139,3212)(140,3211)(141,3210)(142,3209)(143,3208)(144,3207)(145,3206)(146,3205)(147,3204)(148,3203)(149,3202)(150,3201)(151,3200)(152,3199)(153,3198)(154,3197)(155,3196)(156,3195)(157,3194)(158,3193)(159,3192)(160,3191)(161,3190)(162,3189)(163,3188)(164,3187)(165,3186)(166,3185)(167,3184)(168,3183)(169,3182)(170,3181)(171,3180)(172,3179)(173,3178)(174,3177)(175,3176)(176,3175)(177,3174)(178,3173)(179,3172)(180,3171)(181,3170)(182,3169)(183,3168)(184,3167)(185,3166)(186,3165)(187,3164)(188,3163)(189,3162)(190,3161)(191,3160)(192,3159)(193,3158)(194,3157)(195,3156)(196,3155)(197,3154)(198,3153)(199,3152)(200,3151)(201,3150)(202,3149)(203,3148)(204,3147)(205,3146)(206,3145)(207,3144)(208,3143)(209,3142)(210,3141)(211,3140)(212,3139)(213,3138)(214,3137)(215,3136)(216,3135)(217,3134)(218,3133)(219,3132)(220,3131)(221,3130)(222,3129)(223,3128)(224,3127)(225,3126)(226,3125)(227,3124)(228,3123)(229,3122)(230,3121)(231,3120)(232,3119)(233,3118)(234,3117)(235,3116)(236,3115)(237,3114)(238,3113)(239,3112)(240,3111)(241,3110)(242,3109)(243,3108)(244,3107)(245,3106)(246,3105)(247,3104)(248,3103)(249,3102)(250,3101)(251,3100)(252,3099)(253,3098)(254,3097)(255,3096)(256,3095)(257,3094)(258,3093)(259,3092)(260,3091)(261,3090)(262,3089)(263,3088)(264,3087)(265,3086)(266,3085)(267,3084)(268,3083)(269,3082)(270,3081)(271,3080)(272,3079)(273,3078)(274,3077)(275,3076)(276,3075)(277,3074)(278,3073)(279,3072)(280,3071)(281,3070)(282,3069)(283,3068)(284,3067)(285,3066)(286,3065)(287,3064)(288,3063)(289,3062)(290,3061)(291,3060)(292,3059)(293,3058)(294,3057)(295,3056)(296,3055)(297,3054)(298,3053)(299,3052)(300,3051)(301,3050)(302,3049)(303,3048)(304,3047)(305,3046)(306,3045)(307,3044)(308,3043)(309,3042)(310,3041)(311,3040)(312,3039)(313,3038)(314,3037)(315,3036)(316,3035)(317,3034)(318,3033)(319,3032)(320,3031)(321,3030)(322,3029)(323,3028)(324,3027)(325,3026)(326,3025)(327,3024)(328,3023)(329,3022)(330,3021)(331,3020)(332,3019)(333,3018)(334,3017)(335,3016)(336,3015)(337,3014)(338,3013)(339,3012)(340,3011)(341,3010)(342,3009)(343,3008)(344,3007)(345,3006)(346,3005)(347,3004)(348,3003)(349,3002)(350,3001)(351,3000)(352,2999)(353,2998)(354,2997)(355,2996)(356,2995)(357,2994)(358,2993)(359,2992)(360,2991)(361,2990)(362,2989)(363,2988)(364,2987)(365,2986)(366,2985)(367,2984)(368,2983)(369,2982)(370,2981)(371,2980)(372,2979)(373,2978)(374,2977)(375,2976)(376,2975)(377,2974)(378,2973)(379,2972)(380,2971)(381,2970)(382,2969)(383,2968)(384,2967)(385,2966)(386,2965)(387,2964)(388,2963)(389,2962)(390,2961)(391,2960)(392,2959)(393,2958)(394,2957)(395,2956)(396,2955)(397,2954)(398,2953)(399,2952)(400,2951)(401,2950)(402,2949)(403,2948)(404,2947)(405,2946)(406,2945)(407,2944)(408,2943)(409,2942)(410,2941)(411,2940)(412,2939)(413,2938)(414,2937)(415,2936)(416,2935)(417,2934)(418,2933)(419,2932)(420,2931)(421,2930)(422,2929)(423,2928)(424,2927)(425,2926)(426,2925)(427,2924)(428,2923)(429,2922)(430,2921)(431,2920)(432,2919)(433,2918)(434,2917)(435,2916)(436,2915)(437,2914)(438,2913)(439,2912)(440,2911)(441,2910)(442,2909)(443,2908)(444,2907)(445,2906)(446,2905)(447,2904)(448,2903)(449,2902)(450,2901)(451,2900)(452,2899)(453,2898)(454,2897)(455,2896)(456,2895)(457,2894)(458,2893)(459,2892)(460,2891)(461,2890)(462,2889)(463,2888)(464,2887)(465,2886)(466,2885)(467,2884)(468,2883)(469,2882)(470,2881)(471,2880)(472,2879)(473,2878)(474,2877)(475,2876)(476,2875)(477,2874)(478,2873)(479,2872)(480,2871)(481,2870)(482,2869)(483,2868)(484,2867)(485,2866)(486,2865)(487,2864)(488,2863)(489,2862)(490,2861)(491,2860)(492,2859)(493,2858)(494,2857)(495,2856)(496,2855)(497,2854)(498,2853)(499,2852)(500,2851)(501,2850)(502,2849)(503,2848)(504,2847)(505,2846)(506,2845)(507,2844)(508,2843)(509,2842)(510,2841)(511,2840)(512,2839)(513,2838)(514,2837)(515,2836)(516,2835)(517,2834)(518,2833)(519,2832)(520,2831)(521,2830)(522,2829)(523,2828)(524,2827)(525,2826)(526,2825)(527,2824)(528,2823)(529,2822)(530,2821)(531,2820)(532,2819)(533,2818)(534,2817)(535,2816)(536,2815)(537,2814)(538,2813)(539,2812)(540,2811)(541,2810)(542,2809)(543,2808)(544,2807)(545,2806)(546,2805)(547,2804)(548,2803)(549,2802)(550,2801)(551,2800)(552,2799)(553,2798)(554,2797)(555,2796)(556,2795)(557,2794)(558,2793)(559,2792)(560,2791)(561,2790)(562,2789)(563,2788)(564,2787)(565,2786)(566,2785)(567,2784)(568,2783)(569,2782)(570,2781)(571,2780)(572,2779)(573,2778)(574,2777)(575,2776)(576,2775)(577,2774)(578,2773)(579,2772)(580,2771)(581,2770)(582,2769)(583,2768)(584,2767)(585,2766)(586,2765)(587,2764)(588,2763)(589,2762)(590,2761)(591,2760)(592,2759)(593,2758)(594,2757)(595,2756)(596,2755)(597,2754)(598,2753)(599,2752)(600,2751)(601,2750)(602,2749)(603,2748)(604,2747)(605,2746)(606,2745)(607,2744)(608,2743)(609,2742)(610,2741)(611,2740)(612,2739)(613,2738)(614,2737)(615,2736)(616,2735)(617,2734)(618,2733)(619,2732)(620,2731)(621,2730)(622,2729)(623,2728)(624,2727)(625,2726)(626,2725)(627,2724)(628,2723)(629,2722)(630,2721)(631,2720)(632,2719)(633,2718)(634,2717)(635,2716)(636,2715)(637,2714)(638,2713)(639,2712)(640,2711)(641,2710)(642,2709)(643,2708)(644,2707)(645,2706)(646,2705)(647,2704)(648,2703)(649,2702)(650,2701)(651,2700)(652,2699)(653,2698)(654,2697)(655,2696)(656,2695)(657,2694)(658,2693)(659,2692)(660,2691)(661,2690)(662,2689)(663,2688)(664,2687)(665,2686)(666,2685)(667,2684)(668,2683)(669,2682)(670,2681)(671,2680)(672,2679)(673,2678)(674,2677)(675,2676)(676,2675)(677,2674)(678,2673)(679,2672)(680,2671)(681,2670)(682,2669)(683,2668)(684,2667)(685,2666)(686,2665)(687,2664)(688,2663)(689,2662)(690,2661)(691,2660)(692,2659)(693,2658)(694,2657)(695,2656)(696,2655)(697,2654)(698,2653)(699,2652)(700,2651)(701,2650)(702,2649)(703,2648)(704,2647)(705,2646)(706,2645)(707,2644)(708,2643)(709,2642)(710,2641)(711,2640)(712,2639)(713,2638)(714,2637)(715,2636)(716,2635)(717,2634)(718,2633)(719,2632)(720,2631)(721,2630)(722,2629)(723,2628)(724,2627)(725,2626)(726,2625)(727,2624)(728,2623)(729,2622)(730,2621)(731,2620)(732,2619)(733,2618)(734,2617)(735,2616)(736,2615)(737,2614)(738,2613)(739,2612)(740,2611)(741,2610)(742,2609)(743,2608)(744,2607)(745,2606)(746,2605)(747,2604)(748,2603)(749,2602)(750,2601)(751,2600)(752,2599)(753,2598)(754,2597)(755,2596)(756,2595)(757,2594)(758,2593)(759,2592)(760,2591)(761,2590)(762,2589)(763,2588)(764,2587)(765,2586)(766,2585)(767,2584)(768,2583)(769,2582)(770,2581)(771,2580)(772,2579)(773,2578)(774,2577)(775,2576)(776,2575)(777,2574)(778,2573)(779,2572)(780,2571)(781,2570)(782,2569)(783,2568)(784,2567)(785,2566)(786,2565)(787,2564)(788,2563)(789,2562)(790,2561)(791,2560)(792,2559)(793,2558)(794,2557)(795,2556)(796,2555)(797,2554)(798,2553)(799,2552)(800,2551)(801,2550)(802,2549)(803,2548)(804,2547)(805,2546)(806,2545)(807,2544)(808,2543)(809,2542)(810,2541)(811,2540)(812,2539)(813,2538)(814,2537)(815,2536)(816,2535)(817,2534)(818,2533)(819,2532)(820,2531)(821,2530)(822,2529)(823,2528)(824,2527)(825,2526)(826,2525)(827,2524)(828,2523)(829,2522)(830,2521)(831,2520)(832,2519)(833,2518)(834,2517)(835,2516)(836,2515)(837,2514)(838,2513)(839,2512)(840,2511)(841,2510)(842,2509)(843,2508)(844,2507)(845,2506)(846,2505)(847,2504)(848,2503)(849,2502)(850,2501)(851,2500)(852,2499)(853,2498)(854,2497)(855,2496)(856,2495)(857,2494)(858,2493)(859,2492)(860,2491)(861,2490)(862,2489)(863,2488)(864,2487)(865,2486)(866,2485)(867,2484)(868,2483)(869,2482)(870,2481)(871,2480)(872,2479)(873,2478)(874,2477)(875,2476)(876,2475)(877,2474)(878,2473)(879,2472)(880,2471)(881,2470)(882,2469)(883,2468)(884,2467)(885,2466)(886,2465)(887,2464)(888,2463)(889,2462)(890,2461)(891,2460)(892,2459)(893,2458)(894,2457)(895,2456)(896,2455)(897,2454)(898,2453)(899,2452)(900,2451)(901,2450)(902,2449)(903,2448)(904,2447)(905,2446)(906,2445)(907,2444)(908,2443)(909,2442)(910,2441)(911,2440)(912,2439)(913,2438)(914,2437)(915,2436)(916,2435)(917,2434)(918,2433)(919,2432)(920,2431)(921,2430)(922,2429)(923,2428)(924,2427)(925,2426)(926,2425)(927,2424)(928,2423)(929,2422)(930,2421)(931,2420)(932,2419)(933,2418)(934,2417)(935,2416)(936,2415)(937,2414)(938,2413)(939,2412)(940,2411)(941,2410)(942,2409)(943,2408)(944,2407)(945,2406)(946,2405)(947,2404)(948,2403)(949,2402)(950,2401)(951,2400)(952,2399)(953,2398)(954,2397)(955,2396)(956,2395)(957,2394)(958,2393)(959,2392)(960,2391)(961,2390)(962,2389)(963,2388)(964,2387)(965,2386)(966,2385)(967,2384)(968,2383)(969,2382)(970,2381)(971,2380)(972,2379)(973,2378)(974,2377)(975,2376)(976,2375)(977,2374)(978,2373)(979,2372)(980,2371)(981,2370)(982,2369)(983,2368)(984,2367)(985,2366)(986,2365)(987,2364)(988,2363)(989,2362)(990,2361)(991,2360)(992,2359)(993,2358)(994,2357)(995,2356)(996,2355)(997,2354)(998,2353)(999,2352)(1000,2351)(1001,2350)(1002,2349)(1003,2348)(1004,2347)(1005,2346)(1006,2345)(1007,2344)(1008,2343)(1009,2342)(1010,2341)(1011,2340)(1012,2339)(1013,2338)(1014,2337)(1015,2336)(1016,2335)(1017,2334)(1018,2333)(1019,2332)(1020,2331)(1021,2330)(1022,2329)(1023,2328)(1024,2327)(1025,2326)(1026,2325)(1027,2324)(1028,2323)(1029,2322)(1030,2321)(1031,2320)(1032,2319)(1033,2318)(1034,2317)(1035,2316)(1036,2315)(1037,2314)(1038,2313)(1039,2312)(1040,2311)(1041,2310)(1042,2309)(1043,2308)(1044,2307)(1045,2306)(1046,2305)(1047,2304)(1048,2303)(1049,2302)(1050,2301)(1051,2300)(1052,2299)(1053,2298)(1054,2297)(1055,2296)(1056,2295)(1057,2294)(1058,2293)(1059,2292)(1060,2291)(1061,2290)(1062,2289)(1063,2288)(1064,2287)(1065,2286)(1066,2285)(1067,2284)(1068,2283)(1069,2282)(1070,2281)(1071,2280)(1072,2279)(1073,2278)(1074,2277)(1075,2276)(1076,2275)(1077,2274)(1078,2273)(1079,2272)(1080,2271)(1081,2270)(1082,2269)(1083,2268)(1084,2267)(1085,2266)(1086,2265)(1087,2264)(1088,2263)(1089,2262)(1090,2261)(1091,2260)(1092,2259)(1093,2258)(1094,2257)(1095,2256)(1096,2255)(1097,2254)(1098,2253)(1099,2252)(1100,2251)(1101,2250)(1102,2249)(1103,2248)(1104,2247)(1105,2246)(1106,2245)(1107,2244)(1108,2243)(1109,2242)(1110,2241)(1111,2240)(1112,2239)(1113,2238)(1114,2237)(1115,2236)(1116,2235)(1117,2234)(1118,2233)(1119,2232)(1120,2231)(1121,2230)(1122,2229)(1123,2228)(1124,2227)(1125,2226)(1126,2225)(1127,2224)(1128,2223)(1129,2222)(1130,2221)(1131,2220)(1132,2219)(1133,2218)(1134,2217)(1135,2216)(1136,2215)(1137,2214)(1138,2213)(1139,2212)(1140,2211)(1141,2210)(1142,2209)(1143,2208)(1144,2207)(1145,2206)(1146,2205)(1147,2204)(1148,2203)(1149,2202)(1150,2201)(1151,2200)(1152,2199)(1153,2198)(1154,2197)(1155,2196)(1156,2195)(1157,2194)(1158,2193)(1159,2192)(1160,2191)(1161,2190)(1162,2189)(1163,2188)(1164,2187)(1165,2186)(1166,2185)(1167,2184)(1168,2183)(1169,2182)(1170,2181)(1171,2180)(1172,2179)(1173,2178)(1174,2177)(1175,2176)(1176,2175)(1177,2174)(1178,2173)(1179,2172)(1180,2171)(1181,2170)(1182,2169)(1183,2168)(1184,2167)(1185,2166)(1186,2165)(1187,2164)(1188,2163)(1189,2162)(1190,2161)(1191,2160)(1192,2159)(1193,2158)(1194,2157)(1195,2156)(1196,2155)(1197,2154)(1198,2153)(1199,2152)(1200,2151)(1201,2150)(1202,2149)(1203,2148)(1204,2147)(1205,2146)(1206,2145)(1207,2144)(1208,2143)(1209,2142)(1210,2141)(1211,2140)(1212,2139)(1213,2138)(1214,2137)(1215,2136)(1216,2135)(1217,2134)(1218,2133)(1219,2132)(1220,2131)(1221,2130)(1222,2129)(1223,2128)(1224,2127)(1225,2126)(1226,2125)(1227,2124)(1228,2123)(1229,2122)(1230,2121)(1231,2120)(1232,2119)(1233,2118)(1234,2117)(1235,2116)(1236,2115)(1237,2114)(1238,2113)(1239,2112)(1240,2111)(1241,2110)(1242,2109)(1243,2108)(1244,2107)(1245,2106)(1246,2105)(1247,2104)(1248,2103)(1249,2102)(1250,2101)(1251,2100)(1252,2099)(1253,2098)(1254,2097)(1255,2096)(1256,2095)(1257,2094)(1258,2093)(1259,2092)(1260,2091)(1261,2090)(1262,2089)(1263,2088)(1264,2087)(1265,2086)(1266,2085)(1267,2084)(1268,2083)(1269,2082)(1270,2081)(1271,2080)(1272,2079)(1273,2078)(1274,2077)(1275,2076)(1276,2075)(1277,2074)(1278,2073)(1279,2072)(1280,2071)(1281,2070)(1282,2069)(1283,2068)(1284,2067)(1285,2066)(1286,2065)(1287,2064)(1288,2063)(1289,2062)(1290,2061)(1291,2060)(1292,2059)(1293,2058)(1294,2057)(1295,2056)(1296,2055)(1297,2054)(1298,2053)(1299,2052)(1300,2051)(1301,2050)(1302,2049)(1303,2048)(1304,2047)(1305,2046)(1306,2045)(1307,2044)(1308,2043)(1309,2042)(1310,2041)(1311,2040)(1312,2039)(1313,2038)(1314,2037)(1315,2036)(1316,2035)(1317,2034)(1318,2033)(1319,2032)(1320,2031)(1321,2030)(1322,2029)(1323,2028)(1324,2027)(1325,2026)(1326,2025)(1327,2024)(1328,2023)(1329,2022)(1330,2021)(1331,2020)(1332,2019)(1333,2018)(1334,2017)(1335,2016)(1336,2015)(1337,2014)(1338,2013)(1339,2012)(1340,2011)(1341,2010)(1342,2009)(1343,2008)(1344,2007)(1345,2006)(1346,2005)(1347,2004)(1348,2003)(1349,2002)(1350,2001)(1351,2000)(1352,1999)(1353,1998)(1354,1997)(1355,1996)(1356,1995)(1357,1994)(1358,1993)(1359,1992)(1360,1991)(1361,1990)(1362,1989)(1363,1988)(1364,1987)(1365,1986)(1366,1985)(1367,1984)(1368,1983)(1369,1982)(1370,1981)(1371,1980)(1372,1979)(1373,1978)(1374,1977)(1375,1976)(1376,1975)(1377,1974)(1378,1973)(1379,1972)(1380,1971)(1381,1970)(1382,1969)(1383,1968)(1384,1967)(1385,1966)(1386,1965)(1387,1964)(1388,1963)(1389,1962)(1390,1961)(1391,1960)(1392,1959)(1393,1958)(1394,1957)(1395,1956)(1396,1955)(1397,1954)(1398,1953)(1399,1952)(1400,1951)(1401,1950)(1402,1949)(1403,1948)(1404,1947)(1405,1946)(1406,1945)(1407,1944)(1408,1943)(1409,1942)(1410,1941)(1411,1940)(1412,1939)(1413,1938)(1414,1937)(1415,1936)(1416,1935)(1417,1934)(1418,1933)(1419,1932)(1420,1931)(1421,1930)(1422,1929)(1423,1928)(1424,1927)(1425,1926)(1426,1925)(1427,1924)(1428,1923)(1429,1922)(1430,1921)(1431,1920)(1432,1919)(1433,1918)(1434,1917)(1435,1916)(1436,1915)(1437,1914)(1438,1913)(1439,1912)(1440,1911)(1441,1910)(1442,1909)(1443,1908)(1444,1907)(1445,1906)(1446,1905)(1447,1904)(1448,1903)(1449,1902)(1450,1901)(1451,1900)(1452,1899)(1453,1898)(1454,1897)(1455,1896)(1456,1895)(1457,1894)(1458,1893)(1459,1892)(1460,1891)(1461,1890)(1462,1889)(1463,1888)(1464,1887)(1465,1886)(1466,1885)(1467,1884)(1468,1883)(1469,1882)(1470,1881)(1471,1880)(1472,1879)(1473,1878)(1474,1877)(1475,1876)(1476,1875)(1477,1874)(1478,1873)(1479,1872)(1480,1871)(1481,1870)(1482,1869)(1483,1868)(1484,1867)(1485,1866)(1486,1865)(1487,1864)(1488,1863)(1489,1862)(1490,1861)(1491,1860)(1492,1859)(1493,1858)(1494,1857)(1495,1856)(1496,1855)(1497,1854)(1498,1853)(1499,1852)(1500,1851)(1501,1850)(1502,1849)(1503,1848)(1504,1847)(1505,1846)(1506,1845)(1507,1844)(1508,1843)(1509,1842)(1510,1841)(1511,1840)(1512,1839)(1513,1838)(1514,1837)(1515,1836)(1516,1835)(1517,1834)(1518,1833)(1519,1832)(1520,1831)(1521,1830)(1522,1829)(1523,1828)(1524,1827)(1525,1826)(1526,1825)(1527,1824)(1528,1823)(1529,1822)(1530,1821)(1531,1820)(1532,1819)(1533,1818)(1534,1817)(1535,1816)(1536,1815)(1537,1814)(1538,1813)(1539,1812)(1540,1811)(1541,1810)(1542,1809)(1543,1808)(1544,1807)(1545,1806)(1546,1805)(1547,1804)(1548,1803)(1549,1802)(1550,1801)(1551,1800)(1552,1799)(1553,1798)(1554,1797)(1555,1796)(1556,1795)(1557,1794)(1558,1793)(1559,1792)(1560,1791)(1561,1790)(1562,1789)(1563,1788)(1564,1787)(1565,1786)(1566,1785)(1567,1784)(1568,1783)(1569,1782)(1570,1781)(1571,1780)(1572,1779)(1573,1778)(1574,1777)(1575,1776)(1576,1775)(1577,1774)(1578,1773)(1579,1772)(1580,1771)(1581,1770)(1582,1769)(1583,1768)(1584,1767)(1585,1766)(1586,1765)(1587,1764)(1588,1763)(1589,1762)(1590,1761)(1591,1760)(1592,1759)(1593,1758)(1594,1757)(1595,1756)(1596,1755)(1597,1754)(1598,1753)(1599,1752)(1600,1751)(1601,1750)(1602,1749)(1603,1748)(1604,1747)(1605,1746)(1606,1745)(1607,1744)(1608,1743)(1609,1742)(1610,1741)(1611,1740)(1612,1739)(1613,1738)(1614,1737)(1615,1736)(1616,1735)(1617,1734)(1618,1733)(1619,1732)(1620,1731)(1621,1730)(1622,1729)(1623,1728)(1624,1727)(1625,1726)(1626,1725)(1627,1724)(1628,1723)(1629,1722)(1630,1721)(1631,1720)(1632,1719)(1633,1718)(1634,1717)(1635,1716)(1636,1715)(1637,1714)(1638,1713)(1639,1712)(1640,1711)(1641,1710)(1642,1709)(1643,1708)(1644,1707)(1645,1706)(1646,1705)(1647,1704)(1648,1703)(1649,1702)(1650,1701)(1651,1700)(1652,1699)(1653,1698)(1654,1697)(1655,1696)(1656,1695)(1657,1694)(1658,1693)(1659,1692)(1660,1691)(1661,1690)(1662,1689)(1663,1688)(1664,1687)(1665,1686)(1666,1685)(1667,1684)(1668,1683)(1669,1682)(1670,1681)(1671,1680)(1672,1679)(1673,1678)(1674,1677)(1675,1676)
Polycyclic presentation:
2,3,3343|b^a=b^2,c^a=c^3342
Conjugacy classes & character table
5016 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20058, 5);
Finite Group Databasebeta