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Aliases
Splittings
Subgroups
10 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 4053 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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14)(1544,2513)(1545,2512)(1546,2511)(1547,2510)(1548,2509)(1549,2508)(1550,2507)(1551,2506)(1552,2505)(1553,2504)(1554,2503)(1555,2502)(1556,2501)(1557,2500)(1558,2499)(1559,2498)(1560,2497)(1561,2496)(1562,2495)(1563,2494)(1564,2493)(1565,2492)(1566,2491)(1567,2490)(1568,2489)(1569,2488)(1570,2487)(1571,2486)(1572,2485)(1573,2484)(1574,2483)(1575,2482)(1576,2481)(1577,2480)(1578,2479)(1579,2478)(1580,2477)(1581,2476)(1582,2475)(1583,2474)(1584,2473)(1585,2472)(1586,2471)(1587,2470)(1588,2469)(1589,2468)(1590,2467)(1591,2466)(1592,2465)(1593,2464)(1594,2463)(1595,2462)(1596,2461)(1597,2460)(1598,2459)(1599,2458)(1600,2457)(1601,2456)(1602,2455)(1603,2454)(1604,2453)(1605,2452)(1606,2451)(1607,2450)(1608,2449)(1609,2448)(1610,2447)(1611,2446)(1612,2445)(1613,2444)(1614,2443)(1615,2442)(1616,2441)(1617,2440)(1618,2439)(1619,2438)(1620,2437)(1621,2436)(1622,2435)(1623,2434)(1624,2433)(1625,2432)(1626,2431)(1627,2430)(1628,2429)(1629,2428)(1630,2427)(1631,2426)(1632,2425)(1633,2424)(1634,2423)(1635,2422)(1636,2421)(1637,2420)(1638,2419)(1639,2418)(1640,2417)(1641,2416)(1642,2415)(1643,2414)(1644,2413)(1645,2412)(1646,2411)(1647,2410)(1648,2409)(1649,2408)(1650,2407)(1651,2406)(1652,2405)(1653,2404)(1654,2403)(1655,2402)(1656,2401)(1657,2400)(1658,2399)(1659,2398)(1660,2397)(1661,2396)(1662,2395)(1663,2394)(1664,2393)(1665,2392)(1666,2391)(1667,2390)(1668,2389)(1669,2388)(1670,2387)(1671,2386)(1672,2385)(1673,2384)(1674,2383)(1675,2382)(1676,2381)(1677,2380)(1678,2379)(1679,2378)(1680,2377)(1681,2376)(1682,2375)(1683,2374)(1684,2373)(1685,2372)(1686,2371)(1687,2370)(1688,2369)(1689,2368)(1690,2367)(1691,2366)(1692,2365)(1693,2364)(1694,2363)(1695,2362)(1696,2361)(1697,2360)(1698,2359)(1699,2358)(1700,2357)(1701,2356)(1702,2355)(1703,2354)(1704,2353)(1705,2352)(1706,2351)(1707,2350)(1708,2349)(1709,2348)(1710,2347)(1711,2346)(1712,2345)(1713,2344)(1714,2343)(1715,2342)(1716,2341)(1717,2340)(1718,2339)(1719,2338)(1720,2337)(1721,2336)(1722,2335)(1723,2334)(1724,2333)(1725,2332)(1726,2331)(1727,2330)(1728,2329)(1729,2328)(1730,2327)(1731,2326)(1732,2325)(1733,2324)(1734,2323)(1735,2322)(1736,2321)(1737,2320)(1738,2319)(1739,2318)(1740,2317)(1741,2316)(1742,2315)(1743,2314)(1744,2313)(1745,2312)(1746,2311)(1747,2310)(1748,2309)(1749,2308)(1750,2307)(1751,2306)(1752,2305)(1753,2304)(1754,2303)(1755,2302)(1756,2301)(1757,2300)(1758,2299)(1759,2298)(1760,2297)(1761,2296)(1762,2295)(1763,2294)(1764,2293)(1765,2292)(1766,2291)(1767,2290)(1768,2289)(1769,2288)(1770,2287)(1771,2286)(1772,2285)(1773,2284)(1774,2283)(1775,2282)(1776,2281)(1777,2280)(1778,2279)(1779,2278)(1780,2277)(1781,2276)(1782,2275)(1783,2274)(1784,2273)(1785,2272)(1786,2271)(1787,2270)(1788,2269)(1789,2268)(1790,2267)(1791,2266)(1792,2265)(1793,2264)(1794,2263)(1795,2262)(1796,2261)(1797,2260)(1798,2259)(1799,2258)(1800,2257)(1801,2256)(1802,2255)(1803,2254)(1804,2253)(1805,2252)(1806,2251)(1807,2250)(1808,2249)(1809,2248)(1810,2247)(1811,2246)(1812,2245)(1813,2244)(1814,2243)(1815,2242)(1816,2241)(1817,2240)(1818,2239)(1819,2238)(1820,2237)(1821,2236)(1822,2235)(1823,2234)(1824,2233)(1825,2232)(1826,2231)(1827,2230)(1828,2229)(1829,2228)(1830,2227)(1831,2226)(1832,2225)(1833,2224)(1834,2223)(1835,2222)(1836,2221)(1837,2220)(1838,2219)(1839,2218)(1840,2217)(1841,2216)(1842,2215)(1843,2214)(1844,2213)(1845,2212)(1846,2211)(1847,2210)(1848,2209)(1849,2208)(1850,2207)(1851,2206)(1852,2205)(1853,2204)(1854,2203)(1855,2202)(1856,2201)(1857,2200)(1858,2199)(1859,2198)(1860,2197)(1861,2196)(1862,2195)(1863,2194)(1864,2193)(1865,2192)(1866,2191)(1867,2190)(1868,2189)(1869,2188)(1870,2187)(1871,2186)(1872,2185)(1873,2184)(1874,2183)(1875,2182)(1876,2181)(1877,2180)(1878,2179)(1879,2178)(1880,2177)(1881,2176)(1882,2175)(1883,2174)(1884,2173)(1885,2172)(1886,2171)(1887,2170)(1888,2169)(1889,2168)(1890,2167)(1891,2166)(1892,2165)(1893,2164)(1894,2163)(1895,2162)(1896,2161)(1897,2160)(1898,2159)(1899,2158)(1900,2157)(1901,2156)(1902,2155)(1903,2154)(1904,2153)(1905,2152)(1906,2151)(1907,2150)(1908,2149)(1909,2148)(1910,2147)(1911,2146)(1912,2145)(1913,2144)(1914,2143)(1915,2142)(1916,2141)(1917,2140)(1918,2139)(1919,2138)(1920,2137)(1921,2136)(1922,2135)(1923,2134)(1924,2133)(1925,2132)(1926,2131)(1927,2130)(1928,2129)(1929,2128)(1930,2127)(1931,2126)(1932,2125)(1933,2124)(1934,2123)(1935,2122)(1936,2121)(1937,2120)(1938,2119)(1939,2118)(1940,2117)(1941,2116)(1942,2115)(1943,2114)(1944,2113)(1945,2112)(1946,2111)(1947,2110)(1948,2109)(1949,2108)(1950,2107)(1951,2106)(1952,2105)(1953,2104)(1954,2103)(1955,2102)(1956,2101)(1957,2100)(1958,2099)(1959,2098)(1960,2097)(1961,2096)(1962,2095)(1963,2094)(1964,2093)(1965,2092)(1966,2091)(1967,2090)(1968,2089)(1969,2088)(1970,2087)(1971,2086)(1972,2085)(1973,2084)(1974,2083)(1975,2082)(1976,2081)(1977,2080)(1978,2079)(1979,2078)(1980,2077)(1981,2076)(1982,2075)(1983,2074)(1984,2073)(1985,2072)(1986,2071)(1987,2070)(1988,2069)(1989,2068)(1990,2067)(1991,2066)(1992,2065)(1993,2064)(1994,2063)(1995,2062)(1996,2061)(1997,2060)(1998,2059)(1999,2058)(2000,2057)(2001,2056)(2002,2055)(2003,2054)(2004,2053)(2005,2052)(2006,2051)(2007,2050)(2008,2049)(2009,2048)(2010,2047)(2011,2046)(2012,2045)(2013,2044)(2014,2043)(2015,2042)(2016,2041)(2017,2040)(2018,2039)(2019,2038)(2020,2037)(2021,2036)(2022,2035)(2023,2034)(2024,2033)(2025,2032)(2026,2031)(2027,2030)(2028,2029)
Conjugacy classes & character table
4054 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16204, 3);
Finite Group Databasebeta