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Dic6057 #37564491
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 686 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,686)(16,685)(17,684)(18,683)(19,682)(20,681)(21,680)(22,679)(23,678)(24,677)(25,676)(26,675)(27,674)(28,673)(29,672)(30,671)(31,670)(32,669)(33,668)(34,667)(35,666)(36,665)(37,664)(38,663)(39,662)(40,661)(41,660)(42,659)(43,658)(44,657)(45,656)(46,655)(47,654)(48,653)(49,652)(50,651)(51,650)(52,649)(53,648)(54,647)(55,646)(56,645)(57,644)(58,643)(59,642)(60,641)(61,640)(62,639)(63,638)(64,637)(65,636)(66,635)(67,634)(68,633)(69,632)(70,631)(71,630)(72,629)(73,628)(74,627)(75,626)(76,625)(77,624)(78,623)(79,622)(80,621)(81,620)(82,619)(83,618)(84,617)(85,616)(86,615)(87,614)(88,613)(89,612)(90,611)(91,610)(92,609)(93,608)(94,607)(95,606)(96,605)(97,604)(98,603)(99,602)(100,601)(101,600)(102,599)(103,598)(104,597)(105,596)(106,595)(107,594)(108,593)(109,592)(110,591)(111,590)(112,589)(113,588)(114,587)(115,586)(116,585)(117,584)(118,583)(119,582)(120,581)(121,580)(122,579)(123,578)(124,577)(125,576)(126,575)(127,574)(128,573)(129,572)(130,571)(131,570)(132,569)(133,568)(134,567)(135,566)(136,565)(137,564)(138,563)(139,562)(140,561)(141,560)(142,559)(143,558)(144,557)(145,556)(146,555)(147,554)(148,553)(149,552)(150,551)(151,550)(152,549)(153,548)(154,547)(155,546)(156,545)(157,544)(158,543)(159,542)(160,541)(161,540)(162,539)(163,538)(164,537)(165,536)(166,535)(167,534)(168,533)(169,532)(170,531)(171,530)(172,529)(173,528)(174,527)(175,526)(176,525)(177,524)(178,523)(179,522)(180,521)(181,520)(182,519)(183,518)(184,517)(185,516)(186,515)(187,514)(188,513)(189,512)(190,511)(191,510)(192,509)(193,508)(194,507)(195,506)(196,505)(197,504)(198,503)(199,502)(200,501)(201,500)(202,499)(203,498)(204,497)(205,496)(206,495)(207,494)(208,493)(209,492)(210,491)(211,490)(212,489)(213,488)(214,487)(215,486)(216,485)(217,484)(218,483)(219,482)(220,481)(221,480)(222,479)(223,478)(224,477)(225,476)(226,475)(227,474)(228,473)(229,472)(230,471)(231,470)(232,469)(233,468)(234,467)(235,466)(236,465)(237,464)(238,463)(239,462)(240,461)(241,460)(242,459)(243,458)(244,457)(245,456)(246,455)(247,454)(248,453)(249,452)(250,451)(251,450)(252,449)(253,448)(254,447)(255,446)(256,445)(257,444)(258,443)(259,442)(260,441)(261,440)(262,439)(263,438)(264,437)(265,436)(266,435)(267,434)(268,433)(269,432)(270,431)(271,430)(272,429)(273,428)(274,427)(275,426)(276,425)(277,424)(278,423)(279,422)(280,421)(281,420)(282,419)(283,418)(284,417)(285,416)(286,415)(287,414)(288,413)(289,412)(290,411)(291,410)(292,409)(293,408)(294,407)(295,406)(296,405)(297,404)(298,403)(299,402)(300,401)(301,400)(302,399)(303,398)(304,397)(305,396)(306,395)(307,394)(308,393)(309,392)(310,391)(311,390)(312,389)(313,388)(314,387)(315,386)(316,385)(317,384)(318,383)(319,382)(320,381)(321,380)(322,379)(323,378)(324,377)(325,376)(326,375)(327,374)(328,373)(329,372)(330,371)(331,370)(332,369)(333,368)(334,367)(335,366)(336,365)(337,364)(338,363)(339,362)(340,361)(341,360)(342,359)(343,358)(344,357)(345,356)(346,355)(347,354)(348,353)(349,352)(350,351)
Polycyclic presentation:
2,3,673,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^672,e^a=e^2
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, 6);
Finite Group Databasebeta