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Dic4513 #31825290
Aliases
Splittings
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 4517 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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)(1788,2735)(1789,2734)(1790,2733)(1791,2732)(1792,2731)(1793,2730)(1794,2729)(1795,2728)(1796,2727)(1797,2726)(1798,2725)(1799,2724)(1800,2723)(1801,2722)(1802,2721)(1803,2720)(1804,2719)(1805,2718)(1806,2717)(1807,2716)(1808,2715)(1809,2714)(1810,2713)(1811,2712)(1812,2711)(1813,2710)(1814,2709)(1815,2708)(1816,2707)(1817,2706)(1818,2705)(1819,2704)(1820,2703)(1821,2702)(1822,2701)(1823,2700)(1824,2699)(1825,2698)(1826,2697)(1827,2696)(1828,2695)(1829,2694)(1830,2693)(1831,2692)(1832,2691)(1833,2690)(1834,2689)(1835,2688)(1836,2687)(1837,2686)(1838,2685)(1839,2684)(1840,2683)(1841,2682)(1842,2681)(1843,2680)(1844,2679)(1845,2678)(1846,2677)(1847,2676)(1848,2675)(1849,2674)(1850,2673)(1851,2672)(1852,2671)(1853,2670)(1854,2669)(1855,2668)(1856,2667)(1857,2666)(1858,2665)(1859,2664)(1860,2663)(1861,2662)(1862,2661)(1863,2660)(1864,2659)(1865,2658)(1866,2657)(1867,2656)(1868,2655)(1869,2654)(1870,2653)(1871,2652)(1872,2651)(1873,2650)(1874,2649)(1875,2648)(1876,2647)(1877,2646)(1878,2645)(1879,2644)(1880,2643)(1881,2642)(1882,2641)(1883,2640)(1884,2639)(1885,2638)(1886,2637)(1887,2636)(1888,2635)(1889,2634)(1890,2633)(1891,2632)(1892,2631)(1893,2630)(1894,2629)(1895,2628)(1896,2627)(1897,2626)(1898,2625)(1899,2624)(1900,2623)(1901,2622)(1902,2621)(1903,2620)(1904,2619)(1905,2618)(1906,2617)(1907,2616)(1908,2615)(1909,2614)(1910,2613)(1911,2612)(1912,2611)(1913,2610)(1914,2609)(1915,2608)(1916,2607)(1917,2606)(1918,2605)(1919,2604)(1920,2603)(1921,2602)(1922,2601)(1923,2600)(1924,2599)(1925,2598)(1926,2597)(1927,2596)(1928,2595)(1929,2594)(1930,2593)(1931,2592)(1932,2591)(1933,2590)(1934,2589)(1935,2588)(1936,2587)(1937,2586)(1938,2585)(1939,2584)(1940,2583)(1941,2582)(1942,2581)(1943,2580)(1944,2579)(1945,2578)(1946,2577)(1947,2576)(1948,2575)(1949,2574)(1950,2573)(1951,2572)(1952,2571)(1953,2570)(1954,2569)(1955,2568)(1956,2567)(1957,2566)(1958,2565)(1959,2564)(1960,2563)(1961,2562)(1962,2561)(1963,2560)(1964,2559)(1965,2558)(1966,2557)(1967,2556)(1968,2555)(1969,2554)(1970,2553)(1971,2552)(1972,2551)(1973,2550)(1974,2549)(1975,2548)(1976,2547)(1977,2546)(1978,2545)(1979,2544)(1980,2543)(1981,2542)(1982,2541)(1983,2540)(1984,2539)(1985,2538)(1986,2537)(1987,2536)(1988,2535)(1989,2534)(1990,2533)(1991,2532)(1992,2531)(1993,2530)(1994,2529)(1995,2528)(1996,2527)(1997,2526)(1998,2525)(1999,2524)(2000,2523)(2001,2522)(2002,2521)(2003,2520)(2004,2519)(2005,2518)(2006,2517)(2007,2516)(2008,2515)(2009,2514)(2010,2513)(2011,2512)(2012,2511)(2013,2510)(2014,2509)(2015,2508)(2016,2507)(2017,2506)(2018,2505)(2019,2504)(2020,2503)(2021,2502)(2022,2501)(2023,2500)(2024,2499)(2025,2498)(2026,2497)(2027,2496)(2028,2495)(2029,2494)(2030,2493)(2031,2492)(2032,2491)(2033,2490)(2034,2489)(2035,2488)(2036,2487)(2037,2486)(2038,2485)(2039,2484)(2040,2483)(2041,2482)(2042,2481)(2043,2480)(2044,2479)(2045,2478)(2046,2477)(2047,2476)(2048,2475)(2049,2474)(2050,2473)(2051,2472)(2052,2471)(2053,2470)(2054,2469)(2055,2468)(2056,2467)(2057,2466)(2058,2465)(2059,2464)(2060,2463)(2061,2462)(2062,2461)(2063,2460)(2064,2459)(2065,2458)(2066,2457)(2067,2456)(2068,2455)(2069,2454)(2070,2453)(2071,2452)(2072,2451)(2073,2450)(2074,2449)(2075,2448)(2076,2447)(2077,2446)(2078,2445)(2079,2444)(2080,2443)(2081,2442)(2082,2441)(2083,2440)(2084,2439)(2085,2438)(2086,2437)(2087,2436)(2088,2435)(2089,2434)(2090,2433)(2091,2432)(2092,2431)(2093,2430)(2094,2429)(2095,2428)(2096,2427)(2097,2426)(2098,2425)(2099,2424)(2100,2423)(2101,2422)(2102,2421)(2103,2420)(2104,2419)(2105,2418)(2106,2417)(2107,2416)(2108,2415)(2109,2414)(2110,2413)(2111,2412)(2112,2411)(2113,2410)(2114,2409)(2115,2408)(2116,2407)(2117,2406)(2118,2405)(2119,2404)(2120,2403)(2121,2402)(2122,2401)(2123,2400)(2124,2399)(2125,2398)(2126,2397)(2127,2396)(2128,2395)(2129,2394)(2130,2393)(2131,2392)(2132,2391)(2133,2390)(2134,2389)(2135,2388)(2136,2387)(2137,2386)(2138,2385)(2139,2384)(2140,2383)(2141,2382)(2142,2381)(2143,2380)(2144,2379)(2145,2378)(2146,2377)(2147,2376)(2148,2375)(2149,2374)(2150,2373)(2151,2372)(2152,2371)(2153,2370)(2154,2369)(2155,2368)(2156,2367)(2157,2366)(2158,2365)(2159,2364)(2160,2363)(2161,2362)(2162,2361)(2163,2360)(2164,2359)(2165,2358)(2166,2357)(2167,2356)(2168,2355)(2169,2354)(2170,2353)(2171,2352)(2172,2351)(2173,2350)(2174,2349)(2175,2348)(2176,2347)(2177,2346)(2178,2345)(2179,2344)(2180,2343)(2181,2342)(2182,2341)(2183,2340)(2184,2339)(2185,2338)(2186,2337)(2187,2336)(2188,2335)(2189,2334)(2190,2333)(2191,2332)(2192,2331)(2193,2330)(2194,2329)(2195,2328)(2196,2327)(2197,2326)(2198,2325)(2199,2324)(2200,2323)(2201,2322)(2202,2321)(2203,2320)(2204,2319)(2205,2318)(2206,2317)(2207,2316)(2208,2315)(2209,2314)(2210,2313)(2211,2312)(2212,2311)(2213,2310)(2214,2309)(2215,2308)(2216,2307)(2217,2306)(2218,2305)(2219,2304)(2220,2303)(2221,2302)(2222,2301)(2223,2300)(2224,2299)(2225,2298)(2226,2297)(2227,2296)(2228,2295)(2229,2294)(2230,2293)(2231,2292)(2232,2291)(2233,2290)(2234,2289)(2235,2288)(2236,2287)(2237,2286)(2238,2285)(2239,2284)(2240,2283)(2241,2282)(2242,2281)(2243,2280)(2244,2279)(2245,2278)(2246,2277)(2247,2276)(2248,2275)(2249,2274)(2250,2273)(2251,2272)(2252,2271)(2253,2270)(2254,2269)(2255,2268)(2256,2267)(2257,2266)(2258,2265)(2259,2264)(2260,2263)(2261,2262)
Polycyclic presentation:
2^2,4513|a^2=b,c^a=c^4512
Conjugacy classes & character table
4516 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18052, 1);
Finite Group Databasebeta