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Aliases
Splittings
Subgroups
10 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 4051 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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511)(1545,2510)(1546,2509)(1547,2508)(1548,2507)(1549,2506)(1550,2505)(1551,2504)(1552,2503)(1553,2502)(1554,2501)(1555,2500)(1556,2499)(1557,2498)(1558,2497)(1559,2496)(1560,2495)(1561,2494)(1562,2493)(1563,2492)(1564,2491)(1565,2490)(1566,2489)(1567,2488)(1568,2487)(1569,2486)(1570,2485)(1571,2484)(1572,2483)(1573,2482)(1574,2481)(1575,2480)(1576,2479)(1577,2478)(1578,2477)(1579,2476)(1580,2475)(1581,2474)(1582,2473)(1583,2472)(1584,2471)(1585,2470)(1586,2469)(1587,2468)(1588,2467)(1589,2466)(1590,2465)(1591,2464)(1592,2463)(1593,2462)(1594,2461)(1595,2460)(1596,2459)(1597,2458)(1598,2457)(1599,2456)(1600,2455)(1601,2454)(1602,2453)(1603,2452)(1604,2451)(1605,2450)(1606,2449)(1607,2448)(1608,2447)(1609,2446)(1610,2445)(1611,2444)(1612,2443)(1613,2442)(1614,2441)(1615,2440)(1616,2439)(1617,2438)(1618,2437)(1619,2436)(1620,2435)(1621,2434)(1622,2433)(1623,2432)(1624,2431)(1625,2430)(1626,2429)(1627,2428)(1628,2427)(1629,2426)(1630,2425)(1631,2424)(1632,2423)(1633,2422)(1634,2421)(1635,2420)(1636,2419)(1637,2418)(1638,2417)(1639,2416)(1640,2415)(1641,2414)(1642,2413)(1643,2412)(1644,2411)(1645,2410)(1646,2409)(1647,2408)(1648,2407)(1649,2406)(1650,2405)(1651,2404)(1652,2403)(1653,2402)(1654,2401)(1655,2400)(1656,2399)(1657,2398)(1658,2397)(1659,2396)(1660,2395)(1661,2394)(1662,2393)(1663,2392)(1664,2391)(1665,2390)(1666,2389)(1667,2388)(1668,2387)(1669,2386)(1670,2385)(1671,2384)(1672,2383)(1673,2382)(1674,2381)(1675,2380)(1676,2379)(1677,2378)(1678,2377)(1679,2376)(1680,2375)(1681,2374)(1682,2373)(1683,2372)(1684,2371)(1685,2370)(1686,2369)(1687,2368)(1688,2367)(1689,2366)(1690,2365)(1691,2364)(1692,2363)(1693,2362)(1694,2361)(1695,2360)(1696,2359)(1697,2358)(1698,2357)(1699,2356)(1700,2355)(1701,2354)(1702,2353)(1703,2352)(1704,2351)(1705,2350)(1706,2349)(1707,2348)(1708,2347)(1709,2346)(1710,2345)(1711,2344)(1712,2343)(1713,2342)(1714,2341)(1715,2340)(1716,2339)(1717,2338)(1718,2337)(1719,2336)(1720,2335)(1721,2334)(1722,2333)(1723,2332)(1724,2331)(1725,2330)(1726,2329)(1727,2328)(1728,2327)(1729,2326)(1730,2325)(1731,2324)(1732,2323)(1733,2322)(1734,2321)(1735,2320)(1736,2319)(1737,2318)(1738,2317)(1739,2316)(1740,2315)(1741,2314)(1742,2313)(1743,2312)(1744,2311)(1745,2310)(1746,2309)(1747,2308)(1748,2307)(1749,2306)(1750,2305)(1751,2304)(1752,2303)(1753,2302)(1754,2301)(1755,2300)(1756,2299)(1757,2298)(1758,2297)(1759,2296)(1760,2295)(1761,2294)(1762,2293)(1763,2292)(1764,2291)(1765,2290)(1766,2289)(1767,2288)(1768,2287)(1769,2286)(1770,2285)(1771,2284)(1772,2283)(1773,2282)(1774,2281)(1775,2280)(1776,2279)(1777,2278)(1778,2277)(1779,2276)(1780,2275)(1781,2274)(1782,2273)(1783,2272)(1784,2271)(1785,2270)(1786,2269)(1787,2268)(1788,2267)(1789,2266)(1790,2265)(1791,2264)(1792,2263)(1793,2262)(1794,2261)(1795,2260)(1796,2259)(1797,2258)(1798,2257)(1799,2256)(1800,2255)(1801,2254)(1802,2253)(1803,2252)(1804,2251)(1805,2250)(1806,2249)(1807,2248)(1808,2247)(1809,2246)(1810,2245)(1811,2244)(1812,2243)(1813,2242)(1814,2241)(1815,2240)(1816,2239)(1817,2238)(1818,2237)(1819,2236)(1820,2235)(1821,2234)(1822,2233)(1823,2232)(1824,2231)(1825,2230)(1826,2229)(1827,2228)(1828,2227)(1829,2226)(1830,2225)(1831,2224)(1832,2223)(1833,2222)(1834,2221)(1835,2220)(1836,2219)(1837,2218)(1838,2217)(1839,2216)(1840,2215)(1841,2214)(1842,2213)(1843,2212)(1844,2211)(1845,2210)(1846,2209)(1847,2208)(1848,2207)(1849,2206)(1850,2205)(1851,2204)(1852,2203)(1853,2202)(1854,2201)(1855,2200)(1856,2199)(1857,2198)(1858,2197)(1859,2196)(1860,2195)(1861,2194)(1862,2193)(1863,2192)(1864,2191)(1865,2190)(1866,2189)(1867,2188)(1868,2187)(1869,2186)(1870,2185)(1871,2184)(1872,2183)(1873,2182)(1874,2181)(1875,2180)(1876,2179)(1877,2178)(1878,2177)(1879,2176)(1880,2175)(1881,2174)(1882,2173)(1883,2172)(1884,2171)(1885,2170)(1886,2169)(1887,2168)(1888,2167)(1889,2166)(1890,2165)(1891,2164)(1892,2163)(1893,2162)(1894,2161)(1895,2160)(1896,2159)(1897,2158)(1898,2157)(1899,2156)(1900,2155)(1901,2154)(1902,2153)(1903,2152)(1904,2151)(1905,2150)(1906,2149)(1907,2148)(1908,2147)(1909,2146)(1910,2145)(1911,2144)(1912,2143)(1913,2142)(1914,2141)(1915,2140)(1916,2139)(1917,2138)(1918,2137)(1919,2136)(1920,2135)(1921,2134)(1922,2133)(1923,2132)(1924,2131)(1925,2130)(1926,2129)(1927,2128)(1928,2127)(1929,2126)(1930,2125)(1931,2124)(1932,2123)(1933,2122)(1934,2121)(1935,2120)(1936,2119)(1937,2118)(1938,2117)(1939,2116)(1940,2115)(1941,2114)(1942,2113)(1943,2112)(1944,2111)(1945,2110)(1946,2109)(1947,2108)(1948,2107)(1949,2106)(1950,2105)(1951,2104)(1952,2103)(1953,2102)(1954,2101)(1955,2100)(1956,2099)(1957,2098)(1958,2097)(1959,2096)(1960,2095)(1961,2094)(1962,2093)(1963,2092)(1964,2091)(1965,2090)(1966,2089)(1967,2088)(1968,2087)(1969,2086)(1970,2085)(1971,2084)(1972,2083)(1973,2082)(1974,2081)(1975,2080)(1976,2079)(1977,2078)(1978,2077)(1979,2076)(1980,2075)(1981,2074)(1982,2073)(1983,2072)(1984,2071)(1985,2070)(1986,2069)(1987,2068)(1988,2067)(1989,2066)(1990,2065)(1991,2064)(1992,2063)(1993,2062)(1994,2061)(1995,2060)(1996,2059)(1997,2058)(1998,2057)(1999,2056)(2000,2055)(2001,2054)(2002,2053)(2003,2052)(2004,2051)(2005,2050)(2006,2049)(2007,2048)(2008,2047)(2009,2046)(2010,2045)(2011,2044)(2012,2043)(2013,2042)(2014,2041)(2015,2040)(2016,2039)(2017,2038)(2018,2037)(2019,2036)(2020,2035)(2021,2034)(2022,2033)(2023,2032)(2024,2031)(2025,2030)(2026,2029)(2027,2028)
Conjugacy classes & character table
4052 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16196, 4);
Finite Group Databasebeta