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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 872 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);(4,9)(5,8)(6,7)(11,872)(12,871)(13,870)(14,869)(15,868)(16,867)(17,866)(18,865)(19,864)(20,863)(21,862)(22,861)(23,860)(24,859)(25,858)(26,857)(27,856)(28,855)(29,854)(30,853)(31,852)(32,851)(33,850)(34,849)(35,848)(36,847)(37,846)(38,845)(39,844)(40,843)(41,842)(42,841)(43,840)(44,839)(45,838)(46,837)(47,836)(48,835)(49,834)(50,833)(51,832)(52,831)(53,830)(54,829)(55,828)(56,827)(57,826)(58,825)(59,824)(60,823)(61,822)(62,821)(63,820)(64,819)(65,818)(66,817)(67,816)(68,815)(69,814)(70,813)(71,812)(72,811)(73,810)(74,809)(75,808)(76,807)(77,806)(78,805)(79,804)(80,803)(81,802)(82,801)(83,800)(84,799)(85,798)(86,797)(87,796)(88,795)(89,794)(90,793)(91,792)(92,791)(93,790)(94,789)(95,788)(96,787)(97,786)(98,785)(99,784)(100,783)(101,782)(102,781)(103,780)(104,779)(105,778)(106,777)(107,776)(108,775)(109,774)(110,773)(111,772)(112,771)(113,770)(114,769)(115,768)(116,767)(117,766)(118,765)(119,764)(120,763)(121,762)(122,761)(123,760)(124,759)(125,758)(126,757)(127,756)(128,755)(129,754)(130,753)(131,752)(132,751)(133,750)(134,749)(135,748)(136,747)(137,746)(138,745)(139,744)(140,743)(141,742)(142,741)(143,740)(144,739)(145,738)(146,737)(147,736)(148,735)(149,734)(150,733)(151,732)(152,731)(153,730)(154,729)(155,728)(156,727)(157,726)(158,725)(159,724)(160,723)(161,722)(162,721)(163,720)(164,719)(165,718)(166,717)(167,716)(168,715)(169,714)(170,713)(171,712)(172,711)(173,710)(174,709)(175,708)(176,707)(177,706)(178,705)(179,704)(180,703)(181,702)(182,701)(183,700)(184,699)(185,698)(186,697)(187,696)(188,695)(189,694)(190,693)(191,692)(192,691)(193,690)(194,689)(195,688)(196,687)(197,686)(198,685)(199,684)(200,683)(201,682)(202,681)(203,680)(204,679)(205,678)(206,677)(207,676)(208,675)(209,674)(210,673)(211,672)(212,671)(213,670)(214,669)(215,668)(216,667)(217,666)(218,665)(219,664)(220,663)(221,662)(222,661)(223,660)(224,659)(225,658)(226,657)(227,656)(228,655)(229,654)(230,653)(231,652)(232,651)(233,650)(234,649)(235,648)(236,647)(237,646)(238,645)(239,644)(240,643)(241,642)(242,641)(243,640)(244,639)(245,638)(246,637)(247,636)(248,635)(249,634)(250,633)(251,632)(252,631)(253,630)(254,629)(255,628)(256,627)(257,626)(258,625)(259,624)(260,623)(261,622)(262,621)(263,620)(264,619)(265,618)(266,617)(267,616)(268,615)(269,614)(270,613)(271,612)(272,611)(273,610)(274,609)(275,608)(276,607)(277,606)(278,605)(279,604)(280,603)(281,602)(282,601)(283,600)(284,599)(285,598)(286,597)(287,596)(288,595)(289,594)(290,593)(291,592)(292,591)(293,590)(294,589)(295,588)(296,587)(297,586)(298,585)(299,584)(300,583)(301,582)(302,581)(303,580)(304,579)(305,578)(306,577)(307,576)(308,575)(309,574)(310,573)(311,572)(312,571)(313,570)(314,569)(315,568)(316,567)(317,566)(318,565)(319,564)(320,563)(321,562)(322,561)(323,560)(324,559)(325,558)(326,557)(327,556)(328,555)(329,554)(330,553)(331,552)(332,551)(333,550)(334,549)(335,548)(336,547)(337,546)(338,545)(339,544)(340,543)(341,542)(342,541)(343,540)(344,539)(345,538)(346,537)(347,536)(348,535)(349,534)(350,533)(351,532)(352,531)(353,530)(354,529)(355,528)(356,527)(357,526)(358,525)(359,524)(360,523)(361,522)(362,521)(363,520)(364,519)(365,518)(366,517)(367,516)(368,515)(369,514)(370,513)(371,512)(372,511)(373,510)(374,509)(375,508)(376,507)(377,506)(378,505)(379,504)(380,503)(381,502)(382,501)(383,500)(384,499)(385,498)(386,497)(387,496)(388,495)(389,494)(390,493)(391,492)(392,491)(393,490)(394,489)(395,488)(396,487)(397,486)(398,485)(399,484)(400,483)(401,482)(402,481)(403,480)(404,479)(405,478)(406,477)(407,476)(408,475)(409,474)(410,473)(411,472)(412,471)(413,470)(414,469)(415,468)(416,467)(417,466)(418,465)(419,464)(420,463)(421,462)(422,461)(423,460)(424,459)(425,458)(426,457)(427,456)(428,455)(429,454)(430,453)(431,452)(432,451)(433,450)(434,449)(435,448)(436,447)(437,446)(438,445)(439,444)(440,443)(441,442)
Conjugacy classes & character table
6044 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24164, 9);
Finite Group Databasebeta