Finite Group DatabasebetaFinite Group Databasebeta| order | 24622 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12311 |
| unambiguous semidirect product | C13⋊D947 |
| unambiguous semidirect product | C947⋊D13 |
| Fitting, socle, derived, Hall | C13×C947 ⋊ C2 |
| Sylow | C947 ⋊ D13 |
| Sylow | C13 ⋊ D947 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C947 | C2 |
| LCS | G ▷ C13×C947 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 960 |
| transitive degree | μt(G) = 12311 |
A minimal faithful permutation representation — 2 generators on 960 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,960)(16,959)(17,958)(18,957)(19,956)(20,955)(21,954)(22,953)(23,952)(24,951)(25,950)(26,949)(27,948)(28,947)(29,946)(30,945)(31,944)(32,943)(33,942)(34,941)(35,940)(36,939)(37,938)(38,937)(39,936)(40,935)(41,934)(42,933)(43,932)(44,931)(45,930)(46,929)(47,928)(48,927)(49,926)(50,925)(51,924)(52,923)(53,922)(54,921)(55,920)(56,919)(57,918)(58,917)(59,916)(60,915)(61,914)(62,913)(63,912)(64,911)(65,910)(66,909)(67,908)(68,907)(69,906)(70,905)(71,904)(72,903)(73,902)(74,901)(75,900)(76,899)(77,898)(78,897)(79,896)(80,895)(81,894)(82,893)(83,892)(84,891)(85,890)(86,889)(87,888)(88,887)(89,886)(90,885)(91,884)(92,883)(93,882)(94,881)(95,880)(96,879)(97,878)(98,877)(99,876)(100,875)(101,874)(102,873)(103,872)(104,871)(105,870)(106,869)(107,868)(108,867)(109,866)(110,865)(111,864)(112,863)(113,862)(114,861)(115,860)(116,859)(117,858)(118,857)(119,856)(120,855)(121,854)(122,853)(123,852)(124,851)(125,850)(126,849)(127,848)(128,847)(129,846)(130,845)(131,844)(132,843)(133,842)(134,841)(135,840)(136,839)(137,838)(138,837)(139,836)(140,835)(141,834)(142,833)(143,832)(144,831)(145,830)(146,829)(147,828)(148,827)(149,826)(150,825)(151,824)(152,823)(153,822)(154,821)(155,820)(156,819)(157,818)(158,817)(159,816)(160,815)(161,814)(162,813)(163,812)(164,811)(165,810)(166,809)(167,808)(168,807)(169,806)(170,805)(171,804)(172,803)(173,802)(174,801)(175,800)(176,799)(177,798)(178,797)(179,796)(180,795)(181,794)(182,793)(183,792)(184,791)(185,790)(186,789)(187,788)(188,787)(189,786)(190,785)(191,784)(192,783)(193,782)(194,781)(195,780)(196,779)(197,778)(198,777)(199,776)(200,775)(201,774)(202,773)(203,772)(204,771)(205,770)(206,769)(207,768)(208,767)(209,766)(210,765)(211,764)(212,763)(213,762)(214,761)(215,760)(216,759)(217,758)(218,757)(219,756)(220,755)(221,754)(222,753)(223,752)(224,751)(225,750)(226,749)(227,748)(228,747)(229,746)(230,745)(231,744)(232,743)(233,742)(234,741)(235,740)(236,739)(237,738)(238,737)(239,736)(240,735)(241,734)(242,733)(243,732)(244,731)(245,730)(246,729)(247,728)(248,727)(249,726)(250,725)(251,724)(252,723)(253,722)(254,721)(255,720)(256,719)(257,718)(258,717)(259,716)(260,715)(261,714)(262,713)(263,712)(264,711)(265,710)(266,709)(267,708)(268,707)(269,706)(270,705)(271,704)(272,703)(273,702)(274,701)(275,700)(276,699)(277,698)(278,697)(279,696)(280,695)(281,694)(282,693)(283,692)(284,691)(285,690)(286,689)(287,688)(288,687)(289,686)(290,685)(291,684)(292,683)(293,682)(294,681)(295,680)(296,679)(297,678)(298,677)(299,676)(300,675)(301,674)(302,673)(303,672)(304,671)(305,670)(306,669)(307,668)(308,667)(309,666)(310,665)(311,664)(312,663)(313,662)(314,661)(315,660)(316,659)(317,658)(318,657)(319,656)(320,655)(321,654)(322,653)(323,652)(324,651)(325,650)(326,649)(327,648)(328,647)(329,646)(330,645)(331,644)(332,643)(333,642)(334,641)(335,640)(336,639)(337,638)(338,637)(339,636)(340,635)(341,634)(342,633)(343,632)(344,631)(345,630)(346,629)(347,628)(348,627)(349,626)(350,625)(351,624)(352,623)(353,622)(354,621)(355,620)(356,619)(357,618)(358,617)(359,616)(360,615)(361,614)(362,613)(363,612)(364,611)(365,610)(366,609)(367,608)(368,607)(369,606)(370,605)(371,604)(372,603)(373,602)(374,601)(375,600)(376,599)(377,598)(378,597)(379,596)(380,595)(381,594)(382,593)(383,592)(384,591)(385,590)(386,589)(387,588)(388,587)(389,586)(390,585)(391,584)(392,583)(393,582)(394,581)(395,580)(396,579)(397,578)(398,577)(399,576)(400,575)(401,574)(402,573)(403,572)(404,571)(405,570)(406,569)(407,568)(408,567)(409,566)(410,565)(411,564)(412,563)(413,562)(414,561)(415,560)(416,559)(417,558)(418,557)(419,556)(420,555)(421,554)(422,553)(423,552)(424,551)(425,550)(426,549)(427,548)(428,547)(429,546)(430,545)(431,544)(432,543)(433,542)(434,541)(435,540)(436,539)(437,538)(438,537)(439,536)(440,535)(441,534)(442,533)(443,532)(444,531)(445,530)(446,529)(447,528)(448,527)(449,526)(450,525)(451,524)(452,523)(453,522)(454,521)(455,520)(456,519)(457,518)(458,517)(459,516)(460,515)(461,514)(462,513)(463,512)(464,511)(465,510)(466,509)(467,508)(468,507)(469,506)(470,505)(471,504)(472,503)(473,502)(474,501)(475,500)(476,499)(477,498)(478,497)(479,496)(480,495)(481,494)(482,493)(483,492)(484,491)(485,490)(486,489)(487,488)Polycyclic presentation:
2,13,947|b^a=b^12,c^a=c^9466157 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24622, 3);