Finite Group DatabasebetaFinite Group Databasebeta| order | 23262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11631 |
| unambiguous semidirect product | C3⋊D3877 |
| unambiguous semidirect product | C3877⋊D3 |
| Fitting, socle, derived, Hall | C3×C3877 ⋊ C2 |
| Sylow | C3877 ⋊ D3 |
| Sylow | C3 ⋊ D3877 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C3877 | C2 |
| LCS | G ▷ C3×C3877 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 3880 |
| transitive degree | μt(G) = 11631 |
A minimal faithful permutation representation — 2 generators on 3880 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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263)(1623,2262)(1624,2261)(1625,2260)(1626,2259)(1627,2258)(1628,2257)(1629,2256)(1630,2255)(1631,2254)(1632,2253)(1633,2252)(1634,2251)(1635,2250)(1636,2249)(1637,2248)(1638,2247)(1639,2246)(1640,2245)(1641,2244)(1642,2243)(1643,2242)(1644,2241)(1645,2240)(1646,2239)(1647,2238)(1648,2237)(1649,2236)(1650,2235)(1651,2234)(1652,2233)(1653,2232)(1654,2231)(1655,2230)(1656,2229)(1657,2228)(1658,2227)(1659,2226)(1660,2225)(1661,2224)(1662,2223)(1663,2222)(1664,2221)(1665,2220)(1666,2219)(1667,2218)(1668,2217)(1669,2216)(1670,2215)(1671,2214)(1672,2213)(1673,2212)(1674,2211)(1675,2210)(1676,2209)(1677,2208)(1678,2207)(1679,2206)(1680,2205)(1681,2204)(1682,2203)(1683,2202)(1684,2201)(1685,2200)(1686,2199)(1687,2198)(1688,2197)(1689,2196)(1690,2195)(1691,2194)(1692,2193)(1693,2192)(1694,2191)(1695,2190)(1696,2189)(1697,2188)(1698,2187)(1699,2186)(1700,2185)(1701,2184)(1702,2183)(1703,2182)(1704,2181)(1705,2180)(1706,2179)(1707,2178)(1708,2177)(1709,2176)(1710,2175)(1711,2174)(1712,2173)(1713,2172)(1714,2171)(1715,2170)(1716,2169)(1717,2168)(1718,2167)(1719,2166)(1720,2165)(1721,2164)(1722,2163)(1723,2162)(1724,2161)(1725,2160)(1726,2159)(1727,2158)(1728,2157)(1729,2156)(1730,2155)(1731,2154)(1732,2153)(1733,2152)(1734,2151)(1735,2150)(1736,2149)(1737,2148)(1738,2147)(1739,2146)(1740,2145)(1741,2144)(1742,2143)(1743,2142)(1744,2141)(1745,2140)(1746,2139)(1747,2138)(1748,2137)(1749,2136)(1750,2135)(1751,2134)(1752,2133)(1753,2132)(1754,2131)(1755,2130)(1756,2129)(1757,2128)(1758,2127)(1759,2126)(1760,2125)(1761,2124)(1762,2123)(1763,2122)(1764,2121)(1765,2120)(1766,2119)(1767,2118)(1768,2117)(1769,2116)(1770,2115)(1771,2114)(1772,2113)(1773,2112)(1774,2111)(1775,2110)(1776,2109)(1777,2108)(1778,2107)(1779,2106)(1780,2105)(1781,2104)(1782,2103)(1783,2102)(1784,2101)(1785,2100)(1786,2099)(1787,2098)(1788,2097)(1789,2096)(1790,2095)(1791,2094)(1792,2093)(1793,2092)(1794,2091)(1795,2090)(1796,2089)(1797,2088)(1798,2087)(1799,2086)(1800,2085)(1801,2084)(1802,2083)(1803,2082)(1804,2081)(1805,2080)(1806,2079)(1807,2078)(1808,2077)(1809,2076)(1810,2075)(1811,2074)(1812,2073)(1813,2072)(1814,2071)(1815,2070)(1816,2069)(1817,2068)(1818,2067)(1819,2066)(1820,2065)(1821,2064)(1822,2063)(1823,2062)(1824,2061)(1825,2060)(1826,2059)(1827,2058)(1828,2057)(1829,2056)(1830,2055)(1831,2054)(1832,2053)(1833,2052)(1834,2051)(1835,2050)(1836,2049)(1837,2048)(1838,2047)(1839,2046)(1840,2045)(1841,2044)(1842,2043)(1843,2042)(1844,2041)(1845,2040)(1846,2039)(1847,2038)(1848,2037)(1849,2036)(1850,2035)(1851,2034)(1852,2033)(1853,2032)(1854,2031)(1855,2030)(1856,2029)(1857,2028)(1858,2027)(1859,2026)(1860,2025)(1861,2024)(1862,2023)(1863,2022)(1864,2021)(1865,2020)(1866,2019)(1867,2018)(1868,2017)(1869,2016)(1870,2015)(1871,2014)(1872,2013)(1873,2012)(1874,2011)(1875,2010)(1876,2009)(1877,2008)(1878,2007)(1879,2006)(1880,2005)(1881,2004)(1882,2003)(1883,2002)(1884,2001)(1885,2000)(1886,1999)(1887,1998)(1888,1997)(1889,1996)(1890,1995)(1891,1994)(1892,1993)(1893,1992)(1894,1991)(1895,1990)(1896,1989)(1897,1988)(1898,1987)(1899,1986)(1900,1985)(1901,1984)(1902,1983)(1903,1982)(1904,1981)(1905,1980)(1906,1979)(1907,1978)(1908,1977)(1909,1976)(1910,1975)(1911,1974)(1912,1973)(1913,1972)(1914,1971)(1915,1970)(1916,1969)(1917,1968)(1918,1967)(1919,1966)(1920,1965)(1921,1964)(1922,1963)(1923,1962)(1924,1961)(1925,1960)(1926,1959)(1927,1958)(1928,1957)(1929,1956)(1930,1955)(1931,1954)(1932,1953)(1933,1952)(1934,1951)(1935,1950)(1936,1949)(1937,1948)(1938,1947)(1939,1946)(1940,1945)(1941,1944)(1942,1943)Polycyclic presentation:
2,3,3877|b^a=b^2,c^a=c^38765817 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23262, 5);