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D12521 #38736723
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 678 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);(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,678)(22,677)(23,676)(24,675)(25,674)(26,673)(27,672)(28,671)(29,670)(30,669)(31,668)(32,667)(33,666)(34,665)(35,664)(36,663)(37,662)(38,661)(39,660)(40,659)(41,658)(42,657)(43,656)(44,655)(45,654)(46,653)(47,652)(48,651)(49,650)(50,649)(51,648)(52,647)(53,646)(54,645)(55,644)(56,643)(57,642)(58,641)(59,640)(60,639)(61,638)(62,637)(63,636)(64,635)(65,634)(66,633)(67,632)(68,631)(69,630)(70,629)(71,628)(72,627)(73,626)(74,625)(75,624)(76,623)(77,622)(78,621)(79,620)(80,619)(81,618)(82,617)(83,616)(84,615)(85,614)(86,613)(87,612)(88,611)(89,610)(90,609)(91,608)(92,607)(93,606)(94,605)(95,604)(96,603)(97,602)(98,601)(99,600)(100,599)(101,598)(102,597)(103,596)(104,595)(105,594)(106,593)(107,592)(108,591)(109,590)(110,589)(111,588)(112,587)(113,586)(114,585)(115,584)(116,583)(117,582)(118,581)(119,580)(120,579)(121,578)(122,577)(123,576)(124,575)(125,574)(126,573)(127,572)(128,571)(129,570)(130,569)(131,568)(132,567)(133,566)(134,565)(135,564)(136,563)(137,562)(138,561)(139,560)(140,559)(141,558)(142,557)(143,556)(144,555)(145,554)(146,553)(147,552)(148,551)(149,550)(150,549)(151,548)(152,547)(153,546)(154,545)(155,544)(156,543)(157,542)(158,541)(159,540)(160,539)(161,538)(162,537)(163,536)(164,535)(165,534)(166,533)(167,532)(168,531)(169,530)(170,529)(171,528)(172,527)(173,526)(174,525)(175,524)(176,523)(177,522)(178,521)(179,520)(180,519)(181,518)(182,517)(183,516)(184,515)(185,514)(186,513)(187,512)(188,511)(189,510)(190,509)(191,508)(192,507)(193,506)(194,505)(195,504)(196,503)(197,502)(198,501)(199,500)(200,499)(201,498)(202,497)(203,496)(204,495)(205,494)(206,493)(207,492)(208,491)(209,490)(210,489)(211,488)(212,487)(213,486)(214,485)(215,484)(216,483)(217,482)(218,481)(219,480)(220,479)(221,478)(222,477)(223,476)(224,475)(225,474)(226,473)(227,472)(228,471)(229,470)(230,469)(231,468)(232,467)(233,466)(234,465)(235,464)(236,463)(237,462)(238,461)(239,460)(240,459)(241,458)(242,457)(243,456)(244,455)(245,454)(246,453)(247,452)(248,451)(249,450)(250,449)(251,448)(252,447)(253,446)(254,445)(255,444)(256,443)(257,442)(258,441)(259,440)(260,439)(261,438)(262,437)(263,436)(264,435)(265,434)(266,433)(267,432)(268,431)(269,430)(270,429)(271,428)(272,427)(273,426)(274,425)(275,424)(276,423)(277,422)(278,421)(279,420)(280,419)(281,418)(282,417)(283,416)(284,415)(285,414)(286,413)(287,412)(288,411)(289,410)(290,409)(291,408)(292,407)(293,406)(294,405)(295,404)(296,403)(297,402)(298,401)(299,400)(300,399)(301,398)(302,397)(303,396)(304,395)(305,394)(306,393)(307,392)(308,391)(309,390)(310,389)(311,388)(312,387)(313,386)(314,385)(315,384)(316,383)(317,382)(318,381)(319,380)(320,379)(321,378)(322,377)(323,376)(324,375)(325,374)(326,373)(327,372)(328,371)(329,370)(330,369)(331,368)(332,367)(333,366)(334,365)(335,364)(336,363)(337,362)(338,361)(339,360)(340,359)(341,358)(342,357)(343,356)(344,355)(345,354)(346,353)(347,352)(348,351)(349,350)
Polycyclic presentation:
2,19,659|b^a=b^18,c^a=c^658
Conjugacy classes & character table
6262 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25042, 3);
Finite Group Databasebeta