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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 893 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);(5,10)(6,9)(7,8)(12,893)(13,892)(14,891)(15,890)(16,889)(17,888)(18,887)(19,886)(20,885)(21,884)(22,883)(23,882)(24,881)(25,880)(26,879)(27,878)(28,877)(29,876)(30,875)(31,874)(32,873)(33,872)(34,871)(35,870)(36,869)(37,868)(38,867)(39,866)(40,865)(41,864)(42,863)(43,862)(44,861)(45,860)(46,859)(47,858)(48,857)(49,856)(50,855)(51,854)(52,853)(53,852)(54,851)(55,850)(56,849)(57,848)(58,847)(59,846)(60,845)(61,844)(62,843)(63,842)(64,841)(65,840)(66,839)(67,838)(68,837)(69,836)(70,835)(71,834)(72,833)(73,832)(74,831)(75,830)(76,829)(77,828)(78,827)(79,826)(80,825)(81,824)(82,823)(83,822)(84,821)(85,820)(86,819)(87,818)(88,817)(89,816)(90,815)(91,814)(92,813)(93,812)(94,811)(95,810)(96,809)(97,808)(98,807)(99,806)(100,805)(101,804)(102,803)(103,802)(104,801)(105,800)(106,799)(107,798)(108,797)(109,796)(110,795)(111,794)(112,793)(113,792)(114,791)(115,790)(116,789)(117,788)(118,787)(119,786)(120,785)(121,784)(122,783)(123,782)(124,781)(125,780)(126,779)(127,778)(128,777)(129,776)(130,775)(131,774)(132,773)(133,772)(134,771)(135,770)(136,769)(137,768)(138,767)(139,766)(140,765)(141,764)(142,763)(143,762)(144,761)(145,760)(146,759)(147,758)(148,757)(149,756)(150,755)(151,754)(152,753)(153,752)(154,751)(155,750)(156,749)(157,748)(158,747)(159,746)(160,745)(161,744)(162,743)(163,742)(164,741)(165,740)(166,739)(167,738)(168,737)(169,736)(170,735)(171,734)(172,733)(173,732)(174,731)(175,730)(176,729)(177,728)(178,727)(179,726)(180,725)(181,724)(182,723)(183,722)(184,721)(185,720)(186,719)(187,718)(188,717)(189,716)(190,715)(191,714)(192,713)(193,712)(194,711)(195,710)(196,709)(197,708)(198,707)(199,706)(200,705)(201,704)(202,703)(203,702)(204,701)(205,700)(206,699)(207,698)(208,697)(209,696)(210,695)(211,694)(212,693)(213,692)(214,691)(215,690)(216,689)(217,688)(218,687)(219,686)(220,685)(221,684)(222,683)(223,682)(224,681)(225,680)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)(232,673)(233,672)(234,671)(235,670)(236,669)(237,668)(238,667)(239,666)(240,665)(241,664)(242,663)(243,662)(244,661)(245,660)(246,659)(247,658)(248,657)(249,656)(250,655)(251,654)(252,653)(253,652)(254,651)(255,650)(256,649)(257,648)(258,647)(259,646)(260,645)(261,644)(262,643)(263,642)(264,641)(265,640)(266,639)(267,638)(268,637)(269,636)(270,635)(271,634)(272,633)(273,632)(274,631)(275,630)(276,629)(277,628)(278,627)(279,626)(280,625)(281,624)(282,623)(283,622)(284,621)(285,620)(286,619)(287,618)(288,617)(289,616)(290,615)(291,614)(292,613)(293,612)(294,611)(295,610)(296,609)(297,608)(298,607)(299,606)(300,605)(301,604)(302,603)(303,602)(304,601)(305,600)(306,599)(307,598)(308,597)(309,596)(310,595)(311,594)(312,593)(313,592)(314,591)(315,590)(316,589)(317,588)(318,587)(319,586)(320,585)(321,584)(322,583)(323,582)(324,581)(325,580)(326,579)(327,578)(328,577)(329,576)(330,575)(331,574)(332,573)(333,572)(334,571)(335,570)(336,569)(337,568)(338,567)(339,566)(340,565)(341,564)(342,563)(343,562)(344,561)(345,560)(346,559)(347,558)(348,557)(349,556)(350,555)(351,554)(352,553)(353,552)(354,551)(355,550)(356,549)(357,548)(358,547)(359,546)(360,545)(361,544)(362,543)(363,542)(364,541)(365,540)(366,539)(367,538)(368,537)(369,536)(370,535)(371,534)(372,533)(373,532)(374,531)(375,530)(376,529)(377,528)(378,527)(379,526)(380,525)(381,524)(382,523)(383,522)(384,521)(385,520)(386,519)(387,518)(388,517)(389,516)(390,515)(391,514)(392,513)(393,512)(394,511)(395,510)(396,509)(397,508)(398,507)(399,506)(400,505)(401,504)(402,503)(403,502)(404,501)(405,500)(406,499)(407,498)(408,497)(409,496)(410,495)(411,494)(412,493)(413,492)(414,491)(415,490)(416,489)(417,488)(418,487)(419,486)(420,485)(421,484)(422,483)(423,482)(424,481)(425,480)(426,479)(427,478)(428,477)(429,476)(430,475)(431,474)(432,473)(433,472)(434,471)(435,470)(436,469)(437,468)(438,467)(439,466)(440,465)(441,464)(442,463)(443,462)(444,461)(445,460)(446,459)(447,458)(448,457)(449,456)(450,455)(451,454)(452,453)
Conjugacy classes & character table
9276 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37086, 10);
Finite Group Databasebeta