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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 718 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);(4,9)(5,8)(6,7)(11,718)(12,717)(13,716)(14,715)(15,714)(16,713)(17,712)(18,711)(19,710)(20,709)(21,708)(22,707)(23,706)(24,705)(25,704)(26,703)(27,702)(28,701)(29,700)(30,699)(31,698)(32,697)(33,696)(34,695)(35,694)(36,693)(37,692)(38,691)(39,690)(40,689)(41,688)(42,687)(43,686)(44,685)(45,684)(46,683)(47,682)(48,681)(49,680)(50,679)(51,678)(52,677)(53,676)(54,675)(55,674)(56,673)(57,672)(58,671)(59,670)(60,669)(61,668)(62,667)(63,666)(64,665)(65,664)(66,663)(67,662)(68,661)(69,660)(70,659)(71,658)(72,657)(73,656)(74,655)(75,654)(76,653)(77,652)(78,651)(79,650)(80,649)(81,648)(82,647)(83,646)(84,645)(85,644)(86,643)(87,642)(88,641)(89,640)(90,639)(91,638)(92,637)(93,636)(94,635)(95,634)(96,633)(97,632)(98,631)(99,630)(100,629)(101,628)(102,627)(103,626)(104,625)(105,624)(106,623)(107,622)(108,621)(109,620)(110,619)(111,618)(112,617)(113,616)(114,615)(115,614)(116,613)(117,612)(118,611)(119,610)(120,609)(121,608)(122,607)(123,606)(124,605)(125,604)(126,603)(127,602)(128,601)(129,600)(130,599)(131,598)(132,597)(133,596)(134,595)(135,594)(136,593)(137,592)(138,591)(139,590)(140,589)(141,588)(142,587)(143,586)(144,585)(145,584)(146,583)(147,582)(148,581)(149,580)(150,579)(151,578)(152,577)(153,576)(154,575)(155,574)(156,573)(157,572)(158,571)(159,570)(160,569)(161,568)(162,567)(163,566)(164,565)(165,564)(166,563)(167,562)(168,561)(169,560)(170,559)(171,558)(172,557)(173,556)(174,555)(175,554)(176,553)(177,552)(178,551)(179,550)(180,549)(181,548)(182,547)(183,546)(184,545)(185,544)(186,543)(187,542)(188,541)(189,540)(190,539)(191,538)(192,537)(193,536)(194,535)(195,534)(196,533)(197,532)(198,531)(199,530)(200,529)(201,528)(202,527)(203,526)(204,525)(205,524)(206,523)(207,522)(208,521)(209,520)(210,519)(211,518)(212,517)(213,516)(214,515)(215,514)(216,513)(217,512)(218,511)(219,510)(220,509)(221,508)(222,507)(223,506)(224,505)(225,504)(226,503)(227,502)(228,501)(229,500)(230,499)(231,498)(232,497)(233,496)(234,495)(235,494)(236,493)(237,492)(238,491)(239,490)(240,489)(241,488)(242,487)(243,486)(244,485)(245,484)(246,483)(247,482)(248,481)(249,480)(250,479)(251,478)(252,477)(253,476)(254,475)(255,474)(256,473)(257,472)(258,471)(259,470)(260,469)(261,468)(262,467)(263,466)(264,465)(265,464)(266,463)(267,462)(268,461)(269,460)(270,459)(271,458)(272,457)(273,456)(274,455)(275,454)(276,453)(277,452)(278,451)(279,450)(280,449)(281,448)(282,447)(283,446)(284,445)(285,444)(286,443)(287,442)(288,441)(289,440)(290,439)(291,438)(292,437)(293,436)(294,435)(295,434)(296,433)(297,432)(298,431)(299,430)(300,429)(301,428)(302,427)(303,426)(304,425)(305,424)(306,423)(307,422)(308,421)(309,420)(310,419)(311,418)(312,417)(313,416)(314,415)(315,414)(316,413)(317,412)(318,411)(319,410)(320,409)(321,408)(322,407)(323,406)(324,405)(325,404)(326,403)(327,402)(328,401)(329,400)(330,399)(331,398)(332,397)(333,396)(334,395)(335,394)(336,393)(337,392)(338,391)(339,390)(340,389)(341,388)(342,387)(343,386)(344,385)(345,384)(346,383)(347,382)(348,381)(349,380)(350,379)(351,378)(352,377)(353,376)(354,375)(355,374)(356,373)(357,372)(358,371)(359,370)(360,369)(361,368)(362,367)(363,366)(364,365)
Conjugacy classes & character table
4966 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19852, 9);
Finite Group Databasebeta