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Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 684 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);(4,11)(5,10)(6,9)(7,8)(13,684)(14,683)(15,682)(16,681)(17,680)(18,679)(19,678)(20,677)(21,676)(22,675)(23,674)(24,673)(25,672)(26,671)(27,670)(28,669)(29,668)(30,667)(31,666)(32,665)(33,664)(34,663)(35,662)(36,661)(37,660)(38,659)(39,658)(40,657)(41,656)(42,655)(43,654)(44,653)(45,652)(46,651)(47,650)(48,649)(49,648)(50,647)(51,646)(52,645)(53,644)(54,643)(55,642)(56,641)(57,640)(58,639)(59,638)(60,637)(61,636)(62,635)(63,634)(64,633)(65,632)(66,631)(67,630)(68,629)(69,628)(70,627)(71,626)(72,625)(73,624)(74,623)(75,622)(76,621)(77,620)(78,619)(79,618)(80,617)(81,616)(82,615)(83,614)(84,613)(85,612)(86,611)(87,610)(88,609)(89,608)(90,607)(91,606)(92,605)(93,604)(94,603)(95,602)(96,601)(97,600)(98,599)(99,598)(100,597)(101,596)(102,595)(103,594)(104,593)(105,592)(106,591)(107,590)(108,589)(109,588)(110,587)(111,586)(112,585)(113,584)(114,583)(115,582)(116,581)(117,580)(118,579)(119,578)(120,577)(121,576)(122,575)(123,574)(124,573)(125,572)(126,571)(127,570)(128,569)(129,568)(130,567)(131,566)(132,565)(133,564)(134,563)(135,562)(136,561)(137,560)(138,559)(139,558)(140,557)(141,556)(142,555)(143,554)(144,553)(145,552)(146,551)(147,550)(148,549)(149,548)(150,547)(151,546)(152,545)(153,544)(154,543)(155,542)(156,541)(157,540)(158,539)(159,538)(160,537)(161,536)(162,535)(163,534)(164,533)(165,532)(166,531)(167,530)(168,529)(169,528)(170,527)(171,526)(172,525)(173,524)(174,523)(175,522)(176,521)(177,520)(178,519)(179,518)(180,517)(181,516)(182,515)(183,514)(184,513)(185,512)(186,511)(187,510)(188,509)(189,508)(190,507)(191,506)(192,505)(193,504)(194,503)(195,502)(196,501)(197,500)(198,499)(199,498)(200,497)(201,496)(202,495)(203,494)(204,493)(205,492)(206,491)(207,490)(208,489)(209,488)(210,487)(211,486)(212,485)(213,484)(214,483)(215,482)(216,481)(217,480)(218,479)(219,478)(220,477)(221,476)(222,475)(223,474)(224,473)(225,472)(226,471)(227,470)(228,469)(229,468)(230,467)(231,466)(232,465)(233,464)(234,463)(235,462)(236,461)(237,460)(238,459)(239,458)(240,457)(241,456)(242,455)(243,454)(244,453)(245,452)(246,451)(247,450)(248,449)(249,448)(250,447)(251,446)(252,445)(253,444)(254,443)(255,442)(256,441)(257,440)(258,439)(259,438)(260,437)(261,436)(262,435)(263,434)(264,433)(265,432)(266,431)(267,430)(268,429)(269,428)(270,427)(271,426)(272,425)(273,424)(274,423)(275,422)(276,421)(277,420)(278,419)(279,418)(280,417)(281,416)(282,415)(283,414)(284,413)(285,412)(286,411)(287,410)(288,409)(289,408)(290,407)(291,406)(292,405)(293,404)(294,403)(295,402)(296,401)(297,400)(298,399)(299,398)(300,397)(301,396)(302,395)(303,394)(304,393)(305,392)(306,391)(307,390)(308,389)(309,388)(310,387)(311,386)(312,385)(313,384)(314,383)(315,382)(316,381)(317,380)(318,379)(319,378)(320,377)(321,376)(322,375)(323,374)(324,373)(325,372)(326,371)(327,370)(328,369)(329,368)(330,367)(331,366)(332,365)(333,364)(334,363)(335,362)(336,361)(337,360)(338,359)(339,358)(340,357)(341,356)(342,355)(343,354)(344,353)(345,352)(346,351)(347,350)(348,349)
Conjugacy classes & character table
6060 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24228, 16);
Finite Group Databasebeta