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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 890 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);(4,9)(5,8)(6,7)(11,890)(12,889)(13,888)(14,887)(15,886)(16,885)(17,884)(18,883)(19,882)(20,881)(21,880)(22,879)(23,878)(24,877)(25,876)(26,875)(27,874)(28,873)(29,872)(30,871)(31,870)(32,869)(33,868)(34,867)(35,866)(36,865)(37,864)(38,863)(39,862)(40,861)(41,860)(42,859)(43,858)(44,857)(45,856)(46,855)(47,854)(48,853)(49,852)(50,851)(51,850)(52,849)(53,848)(54,847)(55,846)(56,845)(57,844)(58,843)(59,842)(60,841)(61,840)(62,839)(63,838)(64,837)(65,836)(66,835)(67,834)(68,833)(69,832)(70,831)(71,830)(72,829)(73,828)(74,827)(75,826)(76,825)(77,824)(78,823)(79,822)(80,821)(81,820)(82,819)(83,818)(84,817)(85,816)(86,815)(87,814)(88,813)(89,812)(90,811)(91,810)(92,809)(93,808)(94,807)(95,806)(96,805)(97,804)(98,803)(99,802)(100,801)(101,800)(102,799)(103,798)(104,797)(105,796)(106,795)(107,794)(108,793)(109,792)(110,791)(111,790)(112,789)(113,788)(114,787)(115,786)(116,785)(117,784)(118,783)(119,782)(120,781)(121,780)(122,779)(123,778)(124,777)(125,776)(126,775)(127,774)(128,773)(129,772)(130,771)(131,770)(132,769)(133,768)(134,767)(135,766)(136,765)(137,764)(138,763)(139,762)(140,761)(141,760)(142,759)(143,758)(144,757)(145,756)(146,755)(147,754)(148,753)(149,752)(150,751)(151,750)(152,749)(153,748)(154,747)(155,746)(156,745)(157,744)(158,743)(159,742)(160,741)(161,740)(162,739)(163,738)(164,737)(165,736)(166,735)(167,734)(168,733)(169,732)(170,731)(171,730)(172,729)(173,728)(174,727)(175,726)(176,725)(177,724)(178,723)(179,722)(180,721)(181,720)(182,719)(183,718)(184,717)(185,716)(186,715)(187,714)(188,713)(189,712)(190,711)(191,710)(192,709)(193,708)(194,707)(195,706)(196,705)(197,704)(198,703)(199,702)(200,701)(201,700)(202,699)(203,698)(204,697)(205,696)(206,695)(207,694)(208,693)(209,692)(210,691)(211,690)(212,689)(213,688)(214,687)(215,686)(216,685)(217,684)(218,683)(219,682)(220,681)(221,680)(222,679)(223,678)(224,677)(225,676)(226,675)(227,674)(228,673)(229,672)(230,671)(231,670)(232,669)(233,668)(234,667)(235,666)(236,665)(237,664)(238,663)(239,662)(240,661)(241,660)(242,659)(243,658)(244,657)(245,656)(246,655)(247,654)(248,653)(249,652)(250,651)(251,650)(252,649)(253,648)(254,647)(255,646)(256,645)(257,644)(258,643)(259,642)(260,641)(261,640)(262,639)(263,638)(264,637)(265,636)(266,635)(267,634)(268,633)(269,632)(270,631)(271,630)(272,629)(273,628)(274,627)(275,626)(276,625)(277,624)(278,623)(279,622)(280,621)(281,620)(282,619)(283,618)(284,617)(285,616)(286,615)(287,614)(288,613)(289,612)(290,611)(291,610)(292,609)(293,608)(294,607)(295,606)(296,605)(297,604)(298,603)(299,602)(300,601)(301,600)(302,599)(303,598)(304,597)(305,596)(306,595)(307,594)(308,593)(309,592)(310,591)(311,590)(312,589)(313,588)(314,587)(315,586)(316,585)(317,584)(318,583)(319,582)(320,581)(321,580)(322,579)(323,578)(324,577)(325,576)(326,575)(327,574)(328,573)(329,572)(330,571)(331,570)(332,569)(333,568)(334,567)(335,566)(336,565)(337,564)(338,563)(339,562)(340,561)(341,560)(342,559)(343,558)(344,557)(345,556)(346,555)(347,554)(348,553)(349,552)(350,551)(351,550)(352,549)(353,548)(354,547)(355,546)(356,545)(357,544)(358,543)(359,542)(360,541)(361,540)(362,539)(363,538)(364,537)(365,536)(366,535)(367,534)(368,533)(369,532)(370,531)(371,530)(372,529)(373,528)(374,527)(375,526)(376,525)(377,524)(378,523)(379,522)(380,521)(381,520)(382,519)(383,518)(384,517)(385,516)(386,515)(387,514)(388,513)(389,512)(390,511)(391,510)(392,509)(393,508)(394,507)(395,506)(396,505)(397,504)(398,503)(399,502)(400,501)(401,500)(402,499)(403,498)(404,497)(405,496)(406,495)(407,494)(408,493)(409,492)(410,491)(411,490)(412,489)(413,488)(414,487)(415,486)(416,485)(417,484)(418,483)(419,482)(420,481)(421,480)(422,479)(423,478)(424,477)(425,476)(426,475)(427,474)(428,473)(429,472)(430,471)(431,470)(432,469)(433,468)(434,467)(435,466)(436,465)(437,464)(438,463)(439,462)(440,461)(441,460)(442,459)(443,458)(444,457)(445,456)(446,455)(447,454)(448,453)(449,452)(450,451)
Conjugacy classes & character table
6170 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24668, 11);
Finite Group Databasebeta