Finite Group DatabasebetaFinite Group Databasebeta| order | 23334 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11667 |
| unambiguous semidirect product | C3⋊D3889 |
| unambiguous semidirect product | C3889⋊D3 |
| Fitting, socle, derived, Hall | C3×C3889 ⋊ C2 |
| Sylow | C3889 ⋊ D3 |
| Sylow | C3 ⋊ D3889 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C3889 | C2 |
| LCS | G ▷ C3×C3889 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 3892 |
| transitive degree | μt(G) = 11667 |
A minimal faithful permutation representation — 2 generators on 3892 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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617,2280)(1618,2279)(1619,2278)(1620,2277)(1621,2276)(1622,2275)(1623,2274)(1624,2273)(1625,2272)(1626,2271)(1627,2270)(1628,2269)(1629,2268)(1630,2267)(1631,2266)(1632,2265)(1633,2264)(1634,2263)(1635,2262)(1636,2261)(1637,2260)(1638,2259)(1639,2258)(1640,2257)(1641,2256)(1642,2255)(1643,2254)(1644,2253)(1645,2252)(1646,2251)(1647,2250)(1648,2249)(1649,2248)(1650,2247)(1651,2246)(1652,2245)(1653,2244)(1654,2243)(1655,2242)(1656,2241)(1657,2240)(1658,2239)(1659,2238)(1660,2237)(1661,2236)(1662,2235)(1663,2234)(1664,2233)(1665,2232)(1666,2231)(1667,2230)(1668,2229)(1669,2228)(1670,2227)(1671,2226)(1672,2225)(1673,2224)(1674,2223)(1675,2222)(1676,2221)(1677,2220)(1678,2219)(1679,2218)(1680,2217)(1681,2216)(1682,2215)(1683,2214)(1684,2213)(1685,2212)(1686,2211)(1687,2210)(1688,2209)(1689,2208)(1690,2207)(1691,2206)(1692,2205)(1693,2204)(1694,2203)(1695,2202)(1696,2201)(1697,2200)(1698,2199)(1699,2198)(1700,2197)(1701,2196)(1702,2195)(1703,2194)(1704,2193)(1705,2192)(1706,2191)(1707,2190)(1708,2189)(1709,2188)(1710,2187)(1711,2186)(1712,2185)(1713,2184)(1714,2183)(1715,2182)(1716,2181)(1717,2180)(1718,2179)(1719,2178)(1720,2177)(1721,2176)(1722,2175)(1723,2174)(1724,2173)(1725,2172)(1726,2171)(1727,2170)(1728,2169)(1729,2168)(1730,2167)(1731,2166)(1732,2165)(1733,2164)(1734,2163)(1735,2162)(1736,2161)(1737,2160)(1738,2159)(1739,2158)(1740,2157)(1741,2156)(1742,2155)(1743,2154)(1744,2153)(1745,2152)(1746,2151)(1747,2150)(1748,2149)(1749,2148)(1750,2147)(1751,2146)(1752,2145)(1753,2144)(1754,2143)(1755,2142)(1756,2141)(1757,2140)(1758,2139)(1759,2138)(1760,2137)(1761,2136)(1762,2135)(1763,2134)(1764,2133)(1765,2132)(1766,2131)(1767,2130)(1768,2129)(1769,2128)(1770,2127)(1771,2126)(1772,2125)(1773,2124)(1774,2123)(1775,2122)(1776,2121)(1777,2120)(1778,2119)(1779,2118)(1780,2117)(1781,2116)(1782,2115)(1783,2114)(1784,2113)(1785,2112)(1786,2111)(1787,2110)(1788,2109)(1789,2108)(1790,2107)(1791,2106)(1792,2105)(1793,2104)(1794,2103)(1795,2102)(1796,2101)(1797,2100)(1798,2099)(1799,2098)(1800,2097)(1801,2096)(1802,2095)(1803,2094)(1804,2093)(1805,2092)(1806,2091)(1807,2090)(1808,2089)(1809,2088)(1810,2087)(1811,2086)(1812,2085)(1813,2084)(1814,2083)(1815,2082)(1816,2081)(1817,2080)(1818,2079)(1819,2078)(1820,2077)(1821,2076)(1822,2075)(1823,2074)(1824,2073)(1825,2072)(1826,2071)(1827,2070)(1828,2069)(1829,2068)(1830,2067)(1831,2066)(1832,2065)(1833,2064)(1834,2063)(1835,2062)(1836,2061)(1837,2060)(1838,2059)(1839,2058)(1840,2057)(1841,2056)(1842,2055)(1843,2054)(1844,2053)(1845,2052)(1846,2051)(1847,2050)(1848,2049)(1849,2048)(1850,2047)(1851,2046)(1852,2045)(1853,2044)(1854,2043)(1855,2042)(1856,2041)(1857,2040)(1858,2039)(1859,2038)(1860,2037)(1861,2036)(1862,2035)(1863,2034)(1864,2033)(1865,2032)(1866,2031)(1867,2030)(1868,2029)(1869,2028)(1870,2027)(1871,2026)(1872,2025)(1873,2024)(1874,2023)(1875,2022)(1876,2021)(1877,2020)(1878,2019)(1879,2018)(1880,2017)(1881,2016)(1882,2015)(1883,2014)(1884,2013)(1885,2012)(1886,2011)(1887,2010)(1888,2009)(1889,2008)(1890,2007)(1891,2006)(1892,2005)(1893,2004)(1894,2003)(1895,2002)(1896,2001)(1897,2000)(1898,1999)(1899,1998)(1900,1997)(1901,1996)(1902,1995)(1903,1994)(1904,1993)(1905,1992)(1906,1991)(1907,1990)(1908,1989)(1909,1988)(1910,1987)(1911,1986)(1912,1985)(1913,1984)(1914,1983)(1915,1982)(1916,1981)(1917,1980)(1918,1979)(1919,1978)(1920,1977)(1921,1976)(1922,1975)(1923,1974)(1924,1973)(1925,1972)(1926,1971)(1927,1970)(1928,1969)(1929,1968)(1930,1967)(1931,1966)(1932,1965)(1933,1964)(1934,1963)(1935,1962)(1936,1961)(1937,1960)(1938,1959)(1939,1958)(1940,1957)(1941,1956)(1942,1955)(1943,1954)(1944,1953)(1945,1952)(1946,1951)(1947,1950)(1948,1949)Polycyclic presentation:
2,3,3889|b^a=b^2,c^a=c^38885835 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23334, 5);