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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 834 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,834)(16,833)(17,832)(18,831)(19,830)(20,829)(21,828)(22,827)(23,826)(24,825)(25,824)(26,823)(27,822)(28,821)(29,820)(30,819)(31,818)(32,817)(33,816)(34,815)(35,814)(36,813)(37,812)(38,811)(39,810)(40,809)(41,808)(42,807)(43,806)(44,805)(45,804)(46,803)(47,802)(48,801)(49,800)(50,799)(51,798)(52,797)(53,796)(54,795)(55,794)(56,793)(57,792)(58,791)(59,790)(60,789)(61,788)(62,787)(63,786)(64,785)(65,784)(66,783)(67,782)(68,781)(69,780)(70,779)(71,778)(72,777)(73,776)(74,775)(75,774)(76,773)(77,772)(78,771)(79,770)(80,769)(81,768)(82,767)(83,766)(84,765)(85,764)(86,763)(87,762)(88,761)(89,760)(90,759)(91,758)(92,757)(93,756)(94,755)(95,754)(96,753)(97,752)(98,751)(99,750)(100,749)(101,748)(102,747)(103,746)(104,745)(105,744)(106,743)(107,742)(108,741)(109,740)(110,739)(111,738)(112,737)(113,736)(114,735)(115,734)(116,733)(117,732)(118,731)(119,730)(120,729)(121,728)(122,727)(123,726)(124,725)(125,724)(126,723)(127,722)(128,721)(129,720)(130,719)(131,718)(132,717)(133,716)(134,715)(135,714)(136,713)(137,712)(138,711)(139,710)(140,709)(141,708)(142,707)(143,706)(144,705)(145,704)(146,703)(147,702)(148,701)(149,700)(150,699)(151,698)(152,697)(153,696)(154,695)(155,694)(156,693)(157,692)(158,691)(159,690)(160,689)(161,688)(162,687)(163,686)(164,685)(165,684)(166,683)(167,682)(168,681)(169,680)(170,679)(171,678)(172,677)(173,676)(174,675)(175,674)(176,673)(177,672)(178,671)(179,670)(180,669)(181,668)(182,667)(183,666)(184,665)(185,664)(186,663)(187,662)(188,661)(189,660)(190,659)(191,658)(192,657)(193,656)(194,655)(195,654)(196,653)(197,652)(198,651)(199,650)(200,649)(201,648)(202,647)(203,646)(204,645)(205,644)(206,643)(207,642)(208,641)(209,640)(210,639)(211,638)(212,637)(213,636)(214,635)(215,634)(216,633)(217,632)(218,631)(219,630)(220,629)(221,628)(222,627)(223,626)(224,625)(225,624)(226,623)(227,622)(228,621)(229,620)(230,619)(231,618)(232,617)(233,616)(234,615)(235,614)(236,613)(237,612)(238,611)(239,610)(240,609)(241,608)(242,607)(243,606)(244,605)(245,604)(246,603)(247,602)(248,601)(249,600)(250,599)(251,598)(252,597)(253,596)(254,595)(255,594)(256,593)(257,592)(258,591)(259,590)(260,589)(261,588)(262,587)(263,586)(264,585)(265,584)(266,583)(267,582)(268,581)(269,580)(270,579)(271,578)(272,577)(273,576)(274,575)(275,574)(276,573)(277,572)(278,571)(279,570)(280,569)(281,568)(282,567)(283,566)(284,565)(285,564)(286,563)(287,562)(288,561)(289,560)(290,559)(291,558)(292,557)(293,556)(294,555)(295,554)(296,553)(297,552)(298,551)(299,550)(300,549)(301,548)(302,547)(303,546)(304,545)(305,544)(306,543)(307,542)(308,541)(309,540)(310,539)(311,538)(312,537)(313,536)(314,535)(315,534)(316,533)(317,532)(318,531)(319,530)(320,529)(321,528)(322,527)(323,526)(324,525)(325,524)(326,523)(327,522)(328,521)(329,520)(330,519)(331,518)(332,517)(333,516)(334,515)(335,514)(336,513)(337,512)(338,511)(339,510)(340,509)(341,508)(342,507)(343,506)(344,505)(345,504)(346,503)(347,502)(348,501)(349,500)(350,499)(351,498)(352,497)(353,496)(354,495)(355,494)(356,493)(357,492)(358,491)(359,490)(360,489)(361,488)(362,487)(363,486)(364,485)(365,484)(366,483)(367,482)(368,481)(369,480)(370,479)(371,478)(372,477)(373,476)(374,475)(375,474)(376,473)(377,472)(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,463)(387,462)(388,461)(389,460)(390,459)(391,458)(392,457)(393,456)(394,455)(395,454)(396,453)(397,452)(398,451)(399,450)(400,449)(401,448)(402,447)(403,446)(404,445)(405,444)(406,443)(407,442)(408,441)(409,440)(410,439)(411,438)(412,437)(413,436)(414,435)(415,434)(416,433)(417,432)(418,431)(419,430)(420,429)(421,428)(422,427)(423,426)(424,425)
Conjugacy classes & character table
9034 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36124, 11);
Finite Group Databasebeta