← Prev (#37527919) Next (#37527921) →
Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 832 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);(4,9)(5,8)(6,7)(11,832)(12,831)(13,830)(14,829)(15,828)(16,827)(17,826)(18,825)(19,824)(20,823)(21,822)(22,821)(23,820)(24,819)(25,818)(26,817)(27,816)(28,815)(29,814)(30,813)(31,812)(32,811)(33,810)(34,809)(35,808)(36,807)(37,806)(38,805)(39,804)(40,803)(41,802)(42,801)(43,800)(44,799)(45,798)(46,797)(47,796)(48,795)(49,794)(50,793)(51,792)(52,791)(53,790)(54,789)(55,788)(56,787)(57,786)(58,785)(59,784)(60,783)(61,782)(62,781)(63,780)(64,779)(65,778)(66,777)(67,776)(68,775)(69,774)(70,773)(71,772)(72,771)(73,770)(74,769)(75,768)(76,767)(77,766)(78,765)(79,764)(80,763)(81,762)(82,761)(83,760)(84,759)(85,758)(86,757)(87,756)(88,755)(89,754)(90,753)(91,752)(92,751)(93,750)(94,749)(95,748)(96,747)(97,746)(98,745)(99,744)(100,743)(101,742)(102,741)(103,740)(104,739)(105,738)(106,737)(107,736)(108,735)(109,734)(110,733)(111,732)(112,731)(113,730)(114,729)(115,728)(116,727)(117,726)(118,725)(119,724)(120,723)(121,722)(122,721)(123,720)(124,719)(125,718)(126,717)(127,716)(128,715)(129,714)(130,713)(131,712)(132,711)(133,710)(134,709)(135,708)(136,707)(137,706)(138,705)(139,704)(140,703)(141,702)(142,701)(143,700)(144,699)(145,698)(146,697)(147,696)(148,695)(149,694)(150,693)(151,692)(152,691)(153,690)(154,689)(155,688)(156,687)(157,686)(158,685)(159,684)(160,683)(161,682)(162,681)(163,680)(164,679)(165,678)(166,677)(167,676)(168,675)(169,674)(170,673)(171,672)(172,671)(173,670)(174,669)(175,668)(176,667)(177,666)(178,665)(179,664)(180,663)(181,662)(182,661)(183,660)(184,659)(185,658)(186,657)(187,656)(188,655)(189,654)(190,653)(191,652)(192,651)(193,650)(194,649)(195,648)(196,647)(197,646)(198,645)(199,644)(200,643)(201,642)(202,641)(203,640)(204,639)(205,638)(206,637)(207,636)(208,635)(209,634)(210,633)(211,632)(212,631)(213,630)(214,629)(215,628)(216,627)(217,626)(218,625)(219,624)(220,623)(221,622)(222,621)(223,620)(224,619)(225,618)(226,617)(227,616)(228,615)(229,614)(230,613)(231,612)(232,611)(233,610)(234,609)(235,608)(236,607)(237,606)(238,605)(239,604)(240,603)(241,602)(242,601)(243,600)(244,599)(245,598)(246,597)(247,596)(248,595)(249,594)(250,593)(251,592)(252,591)(253,590)(254,589)(255,588)(256,587)(257,586)(258,585)(259,584)(260,583)(261,582)(262,581)(263,580)(264,579)(265,578)(266,577)(267,576)(268,575)(269,574)(270,573)(271,572)(272,571)(273,570)(274,569)(275,568)(276,567)(277,566)(278,565)(279,564)(280,563)(281,562)(282,561)(283,560)(284,559)(285,558)(286,557)(287,556)(288,555)(289,554)(290,553)(291,552)(292,551)(293,550)(294,549)(295,548)(296,547)(297,546)(298,545)(299,544)(300,543)(301,542)(302,541)(303,540)(304,539)(305,538)(306,537)(307,536)(308,535)(309,534)(310,533)(311,532)(312,531)(313,530)(314,529)(315,528)(316,527)(317,526)(318,525)(319,524)(320,523)(321,522)(322,521)(323,520)(324,519)(325,518)(326,517)(327,516)(328,515)(329,514)(330,513)(331,512)(332,511)(333,510)(334,509)(335,508)(336,507)(337,506)(338,505)(339,504)(340,503)(341,502)(342,501)(343,500)(344,499)(345,498)(346,497)(347,496)(348,495)(349,494)(350,493)(351,492)(352,491)(353,490)(354,489)(355,488)(356,487)(357,486)(358,485)(359,484)(360,483)(361,482)(362,481)(363,480)(364,479)(365,478)(366,477)(367,476)(368,475)(369,474)(370,473)(371,472)(372,471)(373,470)(374,469)(375,468)(376,467)(377,466)(378,465)(379,464)(380,463)(381,462)(382,461)(383,460)(384,459)(385,458)(386,457)(387,456)(388,455)(389,454)(390,453)(391,452)(392,451)(393,450)(394,449)(395,448)(396,447)(397,446)(398,445)(399,444)(400,443)(401,442)(402,441)(403,440)(404,439)(405,438)(406,437)(407,436)(408,435)(409,434)(410,433)(411,432)(412,431)(413,430)(414,429)(415,428)(416,427)(417,426)(418,425)(419,424)(420,423)(421,422)
Conjugacy classes & character table
5764 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23044, 9);
Finite Group Databasebeta