Finite Group DatabasebetaFinite Group Databasebeta| order | 23914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11957 |
| unambiguous semidirect product | C11⋊D1087 |
| unambiguous semidirect product | C1087⋊D11 |
| Fitting, socle, derived, Hall | C11×C1087 ⋊ C2 |
| Sylow | C1087 ⋊ D11 |
| Sylow | C11 ⋊ D1087 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C1087 | C2 |
| LCS | G ▷ C11×C1087 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1098 |
| transitive degree | μt(G) = 11957 |
A minimal faithful permutation representation — 2 generators on 1098 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,1098)(14,1097)(15,1096)(16,1095)(17,1094)(18,1093)(19,1092)(20,1091)(21,1090)(22,1089)(23,1088)(24,1087)(25,1086)(26,1085)(27,1084)(28,1083)(29,1082)(30,1081)(31,1080)(32,1079)(33,1078)(34,1077)(35,1076)(36,1075)(37,1074)(38,1073)(39,1072)(40,1071)(41,1070)(42,1069)(43,1068)(44,1067)(45,1066)(46,1065)(47,1064)(48,1063)(49,1062)(50,1061)(51,1060)(52,1059)(53,1058)(54,1057)(55,1056)(56,1055)(57,1054)(58,1053)(59,1052)(60,1051)(61,1050)(62,1049)(63,1048)(64,1047)(65,1046)(66,1045)(67,1044)(68,1043)(69,1042)(70,1041)(71,1040)(72,1039)(73,1038)(74,1037)(75,1036)(76,1035)(77,1034)(78,1033)(79,1032)(80,1031)(81,1030)(82,1029)(83,1028)(84,1027)(85,1026)(86,1025)(87,1024)(88,1023)(89,1022)(90,1021)(91,1020)(92,1019)(93,1018)(94,1017)(95,1016)(96,1015)(97,1014)(98,1013)(99,1012)(100,1011)(101,1010)(102,1009)(103,1008)(104,1007)(105,1006)(106,1005)(107,1004)(108,1003)(109,1002)(110,1001)(111,1000)(112,999)(113,998)(114,997)(115,996)(116,995)(117,994)(118,993)(119,992)(120,991)(121,990)(122,989)(123,988)(124,987)(125,986)(126,985)(127,984)(128,983)(129,982)(130,981)(131,980)(132,979)(133,978)(134,977)(135,976)(136,975)(137,974)(138,973)(139,972)(140,971)(141,970)(142,969)(143,968)(144,967)(145,966)(146,965)(147,964)(148,963)(149,962)(150,961)(151,960)(152,959)(153,958)(154,957)(155,956)(156,955)(157,954)(158,953)(159,952)(160,951)(161,950)(162,949)(163,948)(164,947)(165,946)(166,945)(167,944)(168,943)(169,942)(170,941)(171,940)(172,939)(173,938)(174,937)(175,936)(176,935)(177,934)(178,933)(179,932)(180,931)(181,930)(182,929)(183,928)(184,927)(185,926)(186,925)(187,924)(188,923)(189,922)(190,921)(191,920)(192,919)(193,918)(194,917)(195,916)(196,915)(197,914)(198,913)(199,912)(200,911)(201,910)(202,909)(203,908)(204,907)(205,906)(206,905)(207,904)(208,903)(209,902)(210,901)(211,900)(212,899)(213,898)(214,897)(215,896)(216,895)(217,894)(218,893)(219,892)(220,891)(221,890)(222,889)(223,888)(224,887)(225,886)(226,885)(227,884)(228,883)(229,882)(230,881)(231,880)(232,879)(233,878)(234,877)(235,876)(236,875)(237,874)(238,873)(239,872)(240,871)(241,870)(242,869)(243,868)(244,867)(245,866)(246,865)(247,864)(248,863)(249,862)(250,861)(251,860)(252,859)(253,858)(254,857)(255,856)(256,855)(257,854)(258,853)(259,852)(260,851)(261,850)(262,849)(263,848)(264,847)(265,846)(266,845)(267,844)(268,843)(269,842)(270,841)(271,840)(272,839)(273,838)(274,837)(275,836)(276,835)(277,834)(278,833)(279,832)(280,831)(281,830)(282,829)(283,828)(284,827)(285,826)(286,825)(287,824)(288,823)(289,822)(290,821)(291,820)(292,819)(293,818)(294,817)(295,816)(296,815)(297,814)(298,813)(299,812)(300,811)(301,810)(302,809)(303,808)(304,807)(305,806)(306,805)(307,804)(308,803)(309,802)(310,801)(311,800)(312,799)(313,798)(314,797)(315,796)(316,795)(317,794)(318,793)(319,792)(320,791)(321,790)(322,789)(323,788)(324,787)(325,786)(326,785)(327,784)(328,783)(329,782)(330,781)(331,780)(332,779)(333,778)(334,777)(335,776)(336,775)(337,774)(338,773)(339,772)(340,771)(341,770)(342,769)(343,768)(344,767)(345,766)(346,765)(347,764)(348,763)(349,762)(350,761)(351,760)(352,759)(353,758)(354,757)(355,756)(356,755)(357,754)(358,753)(359,752)(360,751)(361,750)(362,749)(363,748)(364,747)(365,746)(366,745)(367,744)(368,743)(369,742)(370,741)(371,740)(372,739)(373,738)(374,737)(375,736)(376,735)(377,734)(378,733)(379,732)(380,731)(381,730)(382,729)(383,728)(384,727)(385,726)(386,725)(387,724)(388,723)(389,722)(390,721)(391,720)(392,719)(393,718)(394,717)(395,716)(396,715)(397,714)(398,713)(399,712)(400,711)(401,710)(402,709)(403,708)(404,707)(405,706)(406,705)(407,704)(408,703)(409,702)(410,701)(411,700)(412,699)(413,698)(414,697)(415,696)(416,695)(417,694)(418,693)(419,692)(420,691)(421,690)(422,689)(423,688)(424,687)(425,686)(426,685)(427,684)(428,683)(429,682)(430,681)(431,680)(432,679)(433,678)(434,677)(435,676)(436,675)(437,674)(438,673)(439,672)(440,671)(441,670)(442,669)(443,668)(444,667)(445,666)(446,665)(447,664)(448,663)(449,662)(450,661)(451,660)(452,659)(453,658)(454,657)(455,656)(456,655)(457,654)(458,653)(459,652)(460,651)(461,650)(462,649)(463,648)(464,647)(465,646)(466,645)(467,644)(468,643)(469,642)(470,641)(471,640)(472,639)(473,638)(474,637)(475,636)(476,635)(477,634)(478,633)(479,632)(480,631)(481,630)(482,629)(483,628)(484,627)(485,626)(486,625)(487,624)(488,623)(489,622)(490,621)(491,620)(492,619)(493,618)(494,617)(495,616)(496,615)(497,614)(498,613)(499,612)(500,611)(501,610)(502,609)(503,608)(504,607)(505,606)(506,605)(507,604)(508,603)(509,602)(510,601)(511,600)(512,599)(513,598)(514,597)(515,596)(516,595)(517,594)(518,593)(519,592)(520,591)(521,590)(522,589)(523,588)(524,587)(525,586)(526,585)(527,584)(528,583)(529,582)(530,581)(531,580)(532,579)(533,578)(534,577)(535,576)(536,575)(537,574)(538,573)(539,572)(540,571)(541,570)(542,569)(543,568)(544,567)(545,566)(546,565)(547,564)(548,563)(549,562)(550,561)(551,560)(552,559)(553,558)(554,557)(555,556)Polycyclic presentation:
2,11,1087|b^a=b^10,c^a=c^10865980 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23914, 3);