Finite Group DatabasebetaFinite Group Databasebeta| order | 24134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12067 |
| unambiguous semidirect product | C11⋊D1097 |
| unambiguous semidirect product | C1097⋊D11 |
| Fitting, socle, derived, Hall | C11×C1097 ⋊ C2 |
| Sylow | C1097 ⋊ D11 |
| Sylow | C11 ⋊ D1097 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C1097 | C2 |
| LCS | G ▷ C11×C1097 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1108 |
| transitive degree | μt(G) = 12067 |
A minimal faithful permutation representation — 2 generators on 1108 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,1108)(14,1107)(15,1106)(16,1105)(17,1104)(18,1103)(19,1102)(20,1101)(21,1100)(22,1099)(23,1098)(24,1097)(25,1096)(26,1095)(27,1094)(28,1093)(29,1092)(30,1091)(31,1090)(32,1089)(33,1088)(34,1087)(35,1086)(36,1085)(37,1084)(38,1083)(39,1082)(40,1081)(41,1080)(42,1079)(43,1078)(44,1077)(45,1076)(46,1075)(47,1074)(48,1073)(49,1072)(50,1071)(51,1070)(52,1069)(53,1068)(54,1067)(55,1066)(56,1065)(57,1064)(58,1063)(59,1062)(60,1061)(61,1060)(62,1059)(63,1058)(64,1057)(65,1056)(66,1055)(67,1054)(68,1053)(69,1052)(70,1051)(71,1050)(72,1049)(73,1048)(74,1047)(75,1046)(76,1045)(77,1044)(78,1043)(79,1042)(80,1041)(81,1040)(82,1039)(83,1038)(84,1037)(85,1036)(86,1035)(87,1034)(88,1033)(89,1032)(90,1031)(91,1030)(92,1029)(93,1028)(94,1027)(95,1026)(96,1025)(97,1024)(98,1023)(99,1022)(100,1021)(101,1020)(102,1019)(103,1018)(104,1017)(105,1016)(106,1015)(107,1014)(108,1013)(109,1012)(110,1011)(111,1010)(112,1009)(113,1008)(114,1007)(115,1006)(116,1005)(117,1004)(118,1003)(119,1002)(120,1001)(121,1000)(122,999)(123,998)(124,997)(125,996)(126,995)(127,994)(128,993)(129,992)(130,991)(131,990)(132,989)(133,988)(134,987)(135,986)(136,985)(137,984)(138,983)(139,982)(140,981)(141,980)(142,979)(143,978)(144,977)(145,976)(146,975)(147,974)(148,973)(149,972)(150,971)(151,970)(152,969)(153,968)(154,967)(155,966)(156,965)(157,964)(158,963)(159,962)(160,961)(161,960)(162,959)(163,958)(164,957)(165,956)(166,955)(167,954)(168,953)(169,952)(170,951)(171,950)(172,949)(173,948)(174,947)(175,946)(176,945)(177,944)(178,943)(179,942)(180,941)(181,940)(182,939)(183,938)(184,937)(185,936)(186,935)(187,934)(188,933)(189,932)(190,931)(191,930)(192,929)(193,928)(194,927)(195,926)(196,925)(197,924)(198,923)(199,922)(200,921)(201,920)(202,919)(203,918)(204,917)(205,916)(206,915)(207,914)(208,913)(209,912)(210,911)(211,910)(212,909)(213,908)(214,907)(215,906)(216,905)(217,904)(218,903)(219,902)(220,901)(221,900)(222,899)(223,898)(224,897)(225,896)(226,895)(227,894)(228,893)(229,892)(230,891)(231,890)(232,889)(233,888)(234,887)(235,886)(236,885)(237,884)(238,883)(239,882)(240,881)(241,880)(242,879)(243,878)(244,877)(245,876)(246,875)(247,874)(248,873)(249,872)(250,871)(251,870)(252,869)(253,868)(254,867)(255,866)(256,865)(257,864)(258,863)(259,862)(260,861)(261,860)(262,859)(263,858)(264,857)(265,856)(266,855)(267,854)(268,853)(269,852)(270,851)(271,850)(272,849)(273,848)(274,847)(275,846)(276,845)(277,844)(278,843)(279,842)(280,841)(281,840)(282,839)(283,838)(284,837)(285,836)(286,835)(287,834)(288,833)(289,832)(290,831)(291,830)(292,829)(293,828)(294,827)(295,826)(296,825)(297,824)(298,823)(299,822)(300,821)(301,820)(302,819)(303,818)(304,817)(305,816)(306,815)(307,814)(308,813)(309,812)(310,811)(311,810)(312,809)(313,808)(314,807)(315,806)(316,805)(317,804)(318,803)(319,802)(320,801)(321,800)(322,799)(323,798)(324,797)(325,796)(326,795)(327,794)(328,793)(329,792)(330,791)(331,790)(332,789)(333,788)(334,787)(335,786)(336,785)(337,784)(338,783)(339,782)(340,781)(341,780)(342,779)(343,778)(344,777)(345,776)(346,775)(347,774)(348,773)(349,772)(350,771)(351,770)(352,769)(353,768)(354,767)(355,766)(356,765)(357,764)(358,763)(359,762)(360,761)(361,760)(362,759)(363,758)(364,757)(365,756)(366,755)(367,754)(368,753)(369,752)(370,751)(371,750)(372,749)(373,748)(374,747)(375,746)(376,745)(377,744)(378,743)(379,742)(380,741)(381,740)(382,739)(383,738)(384,737)(385,736)(386,735)(387,734)(388,733)(389,732)(390,731)(391,730)(392,729)(393,728)(394,727)(395,726)(396,725)(397,724)(398,723)(399,722)(400,721)(401,720)(402,719)(403,718)(404,717)(405,716)(406,715)(407,714)(408,713)(409,712)(410,711)(411,710)(412,709)(413,708)(414,707)(415,706)(416,705)(417,704)(418,703)(419,702)(420,701)(421,700)(422,699)(423,698)(424,697)(425,696)(426,695)(427,694)(428,693)(429,692)(430,691)(431,690)(432,689)(433,688)(434,687)(435,686)(436,685)(437,684)(438,683)(439,682)(440,681)(441,680)(442,679)(443,678)(444,677)(445,676)(446,675)(447,674)(448,673)(449,672)(450,671)(451,670)(452,669)(453,668)(454,667)(455,666)(456,665)(457,664)(458,663)(459,662)(460,661)(461,660)(462,659)(463,658)(464,657)(465,656)(466,655)(467,654)(468,653)(469,652)(470,651)(471,650)(472,649)(473,648)(474,647)(475,646)(476,645)(477,644)(478,643)(479,642)(480,641)(481,640)(482,639)(483,638)(484,637)(485,636)(486,635)(487,634)(488,633)(489,632)(490,631)(491,630)(492,629)(493,628)(494,627)(495,626)(496,625)(497,624)(498,623)(499,622)(500,621)(501,620)(502,619)(503,618)(504,617)(505,616)(506,615)(507,614)(508,613)(509,612)(510,611)(511,610)(512,609)(513,608)(514,607)(515,606)(516,605)(517,604)(518,603)(519,602)(520,601)(521,600)(522,599)(523,598)(524,597)(525,596)(526,595)(527,594)(528,593)(529,592)(530,591)(531,590)(532,589)(533,588)(534,587)(535,586)(536,585)(537,584)(538,583)(539,582)(540,581)(541,580)(542,579)(543,578)(544,577)(545,576)(546,575)(547,574)(548,573)(549,572)(550,571)(551,570)(552,569)(553,568)(554,567)(555,566)(556,565)(557,564)(558,563)(559,562)(560,561)Polycyclic presentation:
2,11,1097|b^a=b^10,c^a=c^10966035 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24134, 3);