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Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 898 points:
(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898);(4,11)(5,10)(6,9)(7,8)(13,898)(14,897)(15,896)(16,895)(17,894)(18,893)(19,892)(20,891)(21,890)(22,889)(23,888)(24,887)(25,886)(26,885)(27,884)(28,883)(29,882)(30,881)(31,880)(32,879)(33,878)(34,877)(35,876)(36,875)(37,874)(38,873)(39,872)(40,871)(41,870)(42,869)(43,868)(44,867)(45,866)(46,865)(47,864)(48,863)(49,862)(50,861)(51,860)(52,859)(53,858)(54,857)(55,856)(56,855)(57,854)(58,853)(59,852)(60,851)(61,850)(62,849)(63,848)(64,847)(65,846)(66,845)(67,844)(68,843)(69,842)(70,841)(71,840)(72,839)(73,838)(74,837)(75,836)(76,835)(77,834)(78,833)(79,832)(80,831)(81,830)(82,829)(83,828)(84,827)(85,826)(86,825)(87,824)(88,823)(89,822)(90,821)(91,820)(92,819)(93,818)(94,817)(95,816)(96,815)(97,814)(98,813)(99,812)(100,811)(101,810)(102,809)(103,808)(104,807)(105,806)(106,805)(107,804)(108,803)(109,802)(110,801)(111,800)(112,799)(113,798)(114,797)(115,796)(116,795)(117,794)(118,793)(119,792)(120,791)(121,790)(122,789)(123,788)(124,787)(125,786)(126,785)(127,784)(128,783)(129,782)(130,781)(131,780)(132,779)(133,778)(134,777)(135,776)(136,775)(137,774)(138,773)(139,772)(140,771)(141,770)(142,769)(143,768)(144,767)(145,766)(146,765)(147,764)(148,763)(149,762)(150,761)(151,760)(152,759)(153,758)(154,757)(155,756)(156,755)(157,754)(158,753)(159,752)(160,751)(161,750)(162,749)(163,748)(164,747)(165,746)(166,745)(167,744)(168,743)(169,742)(170,741)(171,740)(172,739)(173,738)(174,737)(175,736)(176,735)(177,734)(178,733)(179,732)(180,731)(181,730)(182,729)(183,728)(184,727)(185,726)(186,725)(187,724)(188,723)(189,722)(190,721)(191,720)(192,719)(193,718)(194,717)(195,716)(196,715)(197,714)(198,713)(199,712)(200,711)(201,710)(202,709)(203,708)(204,707)(205,706)(206,705)(207,704)(208,703)(209,702)(210,701)(211,700)(212,699)(213,698)(214,697)(215,696)(216,695)(217,694)(218,693)(219,692)(220,691)(221,690)(222,689)(223,688)(224,687)(225,686)(226,685)(227,684)(228,683)(229,682)(230,681)(231,680)(232,679)(233,678)(234,677)(235,676)(236,675)(237,674)(238,673)(239,672)(240,671)(241,670)(242,669)(243,668)(244,667)(245,666)(246,665)(247,664)(248,663)(249,662)(250,661)(251,660)(252,659)(253,658)(254,657)(255,656)(256,655)(257,654)(258,653)(259,652)(260,651)(261,650)(262,649)(263,648)(264,647)(265,646)(266,645)(267,644)(268,643)(269,642)(270,641)(271,640)(272,639)(273,638)(274,637)(275,636)(276,635)(277,634)(278,633)(279,632)(280,631)(281,630)(282,629)(283,628)(284,627)(285,626)(286,625)(287,624)(288,623)(289,622)(290,621)(291,620)(292,619)(293,618)(294,617)(295,616)(296,615)(297,614)(298,613)(299,612)(300,611)(301,610)(302,609)(303,608)(304,607)(305,606)(306,605)(307,604)(308,603)(309,602)(310,601)(311,600)(312,599)(313,598)(314,597)(315,596)(316,595)(317,594)(318,593)(319,592)(320,591)(321,590)(322,589)(323,588)(324,587)(325,586)(326,585)(327,584)(328,583)(329,582)(330,581)(331,580)(332,579)(333,578)(334,577)(335,576)(336,575)(337,574)(338,573)(339,572)(340,571)(341,570)(342,569)(343,568)(344,567)(345,566)(346,565)(347,564)(348,563)(349,562)(350,561)(351,560)(352,559)(353,558)(354,557)(355,556)(356,555)(357,554)(358,553)(359,552)(360,551)(361,550)(362,549)(363,548)(364,547)(365,546)(366,545)(367,544)(368,543)(369,542)(370,541)(371,540)(372,539)(373,538)(374,537)(375,536)(376,535)(377,534)(378,533)(379,532)(380,531)(381,530)(382,529)(383,528)(384,527)(385,526)(386,525)(387,524)(388,523)(389,522)(390,521)(391,520)(392,519)(393,518)(394,517)(395,516)(396,515)(397,514)(398,513)(399,512)(400,511)(401,510)(402,509)(403,508)(404,507)(405,506)(406,505)(407,504)(408,503)(409,502)(410,501)(411,500)(412,499)(413,498)(414,497)(415,496)(416,495)(417,494)(418,493)(419,492)(420,491)(421,490)(422,489)(423,488)(424,487)(425,486)(426,485)(427,484)(428,483)(429,482)(430,481)(431,480)(432,479)(433,478)(434,477)(435,476)(436,475)(437,474)(438,473)(439,472)(440,471)(441,470)(442,469)(443,468)(444,467)(445,466)(446,465)(447,464)(448,463)(449,462)(450,461)(451,460)(452,459)(453,458)(454,457)(455,456)
Conjugacy classes & character table
7986 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31932, 8);
Finite Group Databasebeta