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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 771 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);(5,10)(6,9)(7,8)(12,771)(13,770)(14,769)(15,768)(16,767)(17,766)(18,765)(19,764)(20,763)(21,762)(22,761)(23,760)(24,759)(25,758)(26,757)(27,756)(28,755)(29,754)(30,753)(31,752)(32,751)(33,750)(34,749)(35,748)(36,747)(37,746)(38,745)(39,744)(40,743)(41,742)(42,741)(43,740)(44,739)(45,738)(46,737)(47,736)(48,735)(49,734)(50,733)(51,732)(52,731)(53,730)(54,729)(55,728)(56,727)(57,726)(58,725)(59,724)(60,723)(61,722)(62,721)(63,720)(64,719)(65,718)(66,717)(67,716)(68,715)(69,714)(70,713)(71,712)(72,711)(73,710)(74,709)(75,708)(76,707)(77,706)(78,705)(79,704)(80,703)(81,702)(82,701)(83,700)(84,699)(85,698)(86,697)(87,696)(88,695)(89,694)(90,693)(91,692)(92,691)(93,690)(94,689)(95,688)(96,687)(97,686)(98,685)(99,684)(100,683)(101,682)(102,681)(103,680)(104,679)(105,678)(106,677)(107,676)(108,675)(109,674)(110,673)(111,672)(112,671)(113,670)(114,669)(115,668)(116,667)(117,666)(118,665)(119,664)(120,663)(121,662)(122,661)(123,660)(124,659)(125,658)(126,657)(127,656)(128,655)(129,654)(130,653)(131,652)(132,651)(133,650)(134,649)(135,648)(136,647)(137,646)(138,645)(139,644)(140,643)(141,642)(142,641)(143,640)(144,639)(145,638)(146,637)(147,636)(148,635)(149,634)(150,633)(151,632)(152,631)(153,630)(154,629)(155,628)(156,627)(157,626)(158,625)(159,624)(160,623)(161,622)(162,621)(163,620)(164,619)(165,618)(166,617)(167,616)(168,615)(169,614)(170,613)(171,612)(172,611)(173,610)(174,609)(175,608)(176,607)(177,606)(178,605)(179,604)(180,603)(181,602)(182,601)(183,600)(184,599)(185,598)(186,597)(187,596)(188,595)(189,594)(190,593)(191,592)(192,591)(193,590)(194,589)(195,588)(196,587)(197,586)(198,585)(199,584)(200,583)(201,582)(202,581)(203,580)(204,579)(205,578)(206,577)(207,576)(208,575)(209,574)(210,573)(211,572)(212,571)(213,570)(214,569)(215,568)(216,567)(217,566)(218,565)(219,564)(220,563)(221,562)(222,561)(223,560)(224,559)(225,558)(226,557)(227,556)(228,555)(229,554)(230,553)(231,552)(232,551)(233,550)(234,549)(235,548)(236,547)(237,546)(238,545)(239,544)(240,543)(241,542)(242,541)(243,540)(244,539)(245,538)(246,537)(247,536)(248,535)(249,534)(250,533)(251,532)(252,531)(253,530)(254,529)(255,528)(256,527)(257,526)(258,525)(259,524)(260,523)(261,522)(262,521)(263,520)(264,519)(265,518)(266,517)(267,516)(268,515)(269,514)(270,513)(271,512)(272,511)(273,510)(274,509)(275,508)(276,507)(277,506)(278,505)(279,504)(280,503)(281,502)(282,501)(283,500)(284,499)(285,498)(286,497)(287,496)(288,495)(289,494)(290,493)(291,492)(292,491)(293,490)(294,489)(295,488)(296,487)(297,486)(298,485)(299,484)(300,483)(301,482)(302,481)(303,480)(304,479)(305,478)(306,477)(307,476)(308,475)(309,474)(310,473)(311,472)(312,471)(313,470)(314,469)(315,468)(316,467)(317,466)(318,465)(319,464)(320,463)(321,462)(322,461)(323,460)(324,459)(325,458)(326,457)(327,456)(328,455)(329,454)(330,453)(331,452)(332,451)(333,450)(334,449)(335,448)(336,447)(337,446)(338,445)(339,444)(340,443)(341,442)(342,441)(343,440)(344,439)(345,438)(346,437)(347,436)(348,435)(349,434)(350,433)(351,432)(352,431)(353,430)(354,429)(355,428)(356,427)(357,426)(358,425)(359,424)(360,423)(361,422)(362,421)(363,420)(364,419)(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)(372,411)(373,410)(374,409)(375,408)(376,407)(377,406)(378,405)(379,404)(380,403)(381,402)(382,401)(383,400)(384,399)(385,398)(386,397)(387,396)(388,395)(389,394)(390,393)(391,392)
Conjugacy classes & character table
7995 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31962, 5);
Finite Group Databasebeta