Finite Group DatabasebetaFinite Group Databasebeta| order | 24154 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12077 |
| unambiguous semidirect product | C13⋊D929 |
| unambiguous semidirect product | C929⋊D13 |
| Fitting, socle, derived, Hall | C13×C929 ⋊ C2 |
| Sylow | C929 ⋊ D13 |
| Sylow | C13 ⋊ D929 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C929 | C2 |
| LCS | G ▷ C13×C929 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 942 |
| transitive degree | μt(G) = 12077 |
A minimal faithful permutation representation — 2 generators on 942 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,942)(16,941)(17,940)(18,939)(19,938)(20,937)(21,936)(22,935)(23,934)(24,933)(25,932)(26,931)(27,930)(28,929)(29,928)(30,927)(31,926)(32,925)(33,924)(34,923)(35,922)(36,921)(37,920)(38,919)(39,918)(40,917)(41,916)(42,915)(43,914)(44,913)(45,912)(46,911)(47,910)(48,909)(49,908)(50,907)(51,906)(52,905)(53,904)(54,903)(55,902)(56,901)(57,900)(58,899)(59,898)(60,897)(61,896)(62,895)(63,894)(64,893)(65,892)(66,891)(67,890)(68,889)(69,888)(70,887)(71,886)(72,885)(73,884)(74,883)(75,882)(76,881)(77,880)(78,879)(79,878)(80,877)(81,876)(82,875)(83,874)(84,873)(85,872)(86,871)(87,870)(88,869)(89,868)(90,867)(91,866)(92,865)(93,864)(94,863)(95,862)(96,861)(97,860)(98,859)(99,858)(100,857)(101,856)(102,855)(103,854)(104,853)(105,852)(106,851)(107,850)(108,849)(109,848)(110,847)(111,846)(112,845)(113,844)(114,843)(115,842)(116,841)(117,840)(118,839)(119,838)(120,837)(121,836)(122,835)(123,834)(124,833)(125,832)(126,831)(127,830)(128,829)(129,828)(130,827)(131,826)(132,825)(133,824)(134,823)(135,822)(136,821)(137,820)(138,819)(139,818)(140,817)(141,816)(142,815)(143,814)(144,813)(145,812)(146,811)(147,810)(148,809)(149,808)(150,807)(151,806)(152,805)(153,804)(154,803)(155,802)(156,801)(157,800)(158,799)(159,798)(160,797)(161,796)(162,795)(163,794)(164,793)(165,792)(166,791)(167,790)(168,789)(169,788)(170,787)(171,786)(172,785)(173,784)(174,783)(175,782)(176,781)(177,780)(178,779)(179,778)(180,777)(181,776)(182,775)(183,774)(184,773)(185,772)(186,771)(187,770)(188,769)(189,768)(190,767)(191,766)(192,765)(193,764)(194,763)(195,762)(196,761)(197,760)(198,759)(199,758)(200,757)(201,756)(202,755)(203,754)(204,753)(205,752)(206,751)(207,750)(208,749)(209,748)(210,747)(211,746)(212,745)(213,744)(214,743)(215,742)(216,741)(217,740)(218,739)(219,738)(220,737)(221,736)(222,735)(223,734)(224,733)(225,732)(226,731)(227,730)(228,729)(229,728)(230,727)(231,726)(232,725)(233,724)(234,723)(235,722)(236,721)(237,720)(238,719)(239,718)(240,717)(241,716)(242,715)(243,714)(244,713)(245,712)(246,711)(247,710)(248,709)(249,708)(250,707)(251,706)(252,705)(253,704)(254,703)(255,702)(256,701)(257,700)(258,699)(259,698)(260,697)(261,696)(262,695)(263,694)(264,693)(265,692)(266,691)(267,690)(268,689)(269,688)(270,687)(271,686)(272,685)(273,684)(274,683)(275,682)(276,681)(277,680)(278,679)(279,678)(280,677)(281,676)(282,675)(283,674)(284,673)(285,672)(286,671)(287,670)(288,669)(289,668)(290,667)(291,666)(292,665)(293,664)(294,663)(295,662)(296,661)(297,660)(298,659)(299,658)(300,657)(301,656)(302,655)(303,654)(304,653)(305,652)(306,651)(307,650)(308,649)(309,648)(310,647)(311,646)(312,645)(313,644)(314,643)(315,642)(316,641)(317,640)(318,639)(319,638)(320,637)(321,636)(322,635)(323,634)(324,633)(325,632)(326,631)(327,630)(328,629)(329,628)(330,627)(331,626)(332,625)(333,624)(334,623)(335,622)(336,621)(337,620)(338,619)(339,618)(340,617)(341,616)(342,615)(343,614)(344,613)(345,612)(346,611)(347,610)(348,609)(349,608)(350,607)(351,606)(352,605)(353,604)(354,603)(355,602)(356,601)(357,600)(358,599)(359,598)(360,597)(361,596)(362,595)(363,594)(364,593)(365,592)(366,591)(367,590)(368,589)(369,588)(370,587)(371,586)(372,585)(373,584)(374,583)(375,582)(376,581)(377,580)(378,579)(379,578)(380,577)(381,576)(382,575)(383,574)(384,573)(385,572)(386,571)(387,570)(388,569)(389,568)(390,567)(391,566)(392,565)(393,564)(394,563)(395,562)(396,561)(397,560)(398,559)(399,558)(400,557)(401,556)(402,555)(403,554)(404,553)(405,552)(406,551)(407,550)(408,549)(409,548)(410,547)(411,546)(412,545)(413,544)(414,543)(415,542)(416,541)(417,540)(418,539)(419,538)(420,537)(421,536)(422,535)(423,534)(424,533)(425,532)(426,531)(427,530)(428,529)(429,528)(430,527)(431,526)(432,525)(433,524)(434,523)(435,522)(436,521)(437,520)(438,519)(439,518)(440,517)(441,516)(442,515)(443,514)(444,513)(445,512)(446,511)(447,510)(448,509)(449,508)(450,507)(451,506)(452,505)(453,504)(454,503)(455,502)(456,501)(457,500)(458,499)(459,498)(460,497)(461,496)(462,495)(463,494)(464,493)(465,492)(466,491)(467,490)(468,489)(469,488)(470,487)(471,486)(472,485)(473,484)(474,483)(475,482)(476,481)(477,480)(478,479)Polycyclic presentation:
2,13,929|b^a=b^12,c^a=c^9286040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24154, 3);