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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 794 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);(4,7)(5,6)(9,794)(10,793)(11,792)(12,791)(13,790)(14,789)(15,788)(16,787)(17,786)(18,785)(19,784)(20,783)(21,782)(22,781)(23,780)(24,779)(25,778)(26,777)(27,776)(28,775)(29,774)(30,773)(31,772)(32,771)(33,770)(34,769)(35,768)(36,767)(37,766)(38,765)(39,764)(40,763)(41,762)(42,761)(43,760)(44,759)(45,758)(46,757)(47,756)(48,755)(49,754)(50,753)(51,752)(52,751)(53,750)(54,749)(55,748)(56,747)(57,746)(58,745)(59,744)(60,743)(61,742)(62,741)(63,740)(64,739)(65,738)(66,737)(67,736)(68,735)(69,734)(70,733)(71,732)(72,731)(73,730)(74,729)(75,728)(76,727)(77,726)(78,725)(79,724)(80,723)(81,722)(82,721)(83,720)(84,719)(85,718)(86,717)(87,716)(88,715)(89,714)(90,713)(91,712)(92,711)(93,710)(94,709)(95,708)(96,707)(97,706)(98,705)(99,704)(100,703)(101,702)(102,701)(103,700)(104,699)(105,698)(106,697)(107,696)(108,695)(109,694)(110,693)(111,692)(112,691)(113,690)(114,689)(115,688)(116,687)(117,686)(118,685)(119,684)(120,683)(121,682)(122,681)(123,680)(124,679)(125,678)(126,677)(127,676)(128,675)(129,674)(130,673)(131,672)(132,671)(133,670)(134,669)(135,668)(136,667)(137,666)(138,665)(139,664)(140,663)(141,662)(142,661)(143,660)(144,659)(145,658)(146,657)(147,656)(148,655)(149,654)(150,653)(151,652)(152,651)(153,650)(154,649)(155,648)(156,647)(157,646)(158,645)(159,644)(160,643)(161,642)(162,641)(163,640)(164,639)(165,638)(166,637)(167,636)(168,635)(169,634)(170,633)(171,632)(172,631)(173,630)(174,629)(175,628)(176,627)(177,626)(178,625)(179,624)(180,623)(181,622)(182,621)(183,620)(184,619)(185,618)(186,617)(187,616)(188,615)(189,614)(190,613)(191,612)(192,611)(193,610)(194,609)(195,608)(196,607)(197,606)(198,605)(199,604)(200,603)(201,602)(202,601)(203,600)(204,599)(205,598)(206,597)(207,596)(208,595)(209,594)(210,593)(211,592)(212,591)(213,590)(214,589)(215,588)(216,587)(217,586)(218,585)(219,584)(220,583)(221,582)(222,581)(223,580)(224,579)(225,578)(226,577)(227,576)(228,575)(229,574)(230,573)(231,572)(232,571)(233,570)(234,569)(235,568)(236,567)(237,566)(238,565)(239,564)(240,563)(241,562)(242,561)(243,560)(244,559)(245,558)(246,557)(247,556)(248,555)(249,554)(250,553)(251,552)(252,551)(253,550)(254,549)(255,548)(256,547)(257,546)(258,545)(259,544)(260,543)(261,542)(262,541)(263,540)(264,539)(265,538)(266,537)(267,536)(268,535)(269,534)(270,533)(271,532)(272,531)(273,530)(274,529)(275,528)(276,527)(277,526)(278,525)(279,524)(280,523)(281,522)(282,521)(283,520)(284,519)(285,518)(286,517)(287,516)(288,515)(289,514)(290,513)(291,512)(292,511)(293,510)(294,509)(295,508)(296,507)(297,506)(298,505)(299,504)(300,503)(301,502)(302,501)(303,500)(304,499)(305,498)(306,497)(307,496)(308,495)(309,494)(310,493)(311,492)(312,491)(313,490)(314,489)(315,488)(316,487)(317,486)(318,485)(319,484)(320,483)(321,482)(322,481)(323,480)(324,479)(325,478)(326,477)(327,476)(328,475)(329,474)(330,473)(331,472)(332,471)(333,470)(334,469)(335,468)(336,467)(337,466)(338,465)(339,464)(340,463)(341,462)(342,461)(343,460)(344,459)(345,458)(346,457)(347,456)(348,455)(349,454)(350,453)(351,452)(352,451)(353,450)(354,449)(355,448)(356,447)(357,446)(358,445)(359,444)(360,443)(361,442)(362,441)(363,440)(364,439)(365,438)(366,437)(367,436)(368,435)(369,434)(370,433)(371,432)(372,431)(373,430)(374,429)(375,428)(376,427)(377,426)(378,425)(379,424)(380,423)(381,422)(382,421)(383,420)(384,419)(385,418)(386,417)(387,416)(388,415)(389,414)(390,413)(391,412)(392,411)(393,410)(394,409)(395,408)(396,407)(397,406)(398,405)(399,404)(400,403)(401,402)
Conjugacy classes & character table
3938 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15740, 9);
Finite Group Databasebeta