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D9465 #34038772
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 639 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);(2,3)(5,8)(6,7)(10,639)(11,638)(12,637)(13,636)(14,635)(15,634)(16,633)(17,632)(18,631)(19,630)(20,629)(21,628)(22,627)(23,626)(24,625)(25,624)(26,623)(27,622)(28,621)(29,620)(30,619)(31,618)(32,617)(33,616)(34,615)(35,614)(36,613)(37,612)(38,611)(39,610)(40,609)(41,608)(42,607)(43,606)(44,605)(45,604)(46,603)(47,602)(48,601)(49,600)(50,599)(51,598)(52,597)(53,596)(54,595)(55,594)(56,593)(57,592)(58,591)(59,590)(60,589)(61,588)(62,587)(63,586)(64,585)(65,584)(66,583)(67,582)(68,581)(69,580)(70,579)(71,578)(72,577)(73,576)(74,575)(75,574)(76,573)(77,572)(78,571)(79,570)(80,569)(81,568)(82,567)(83,566)(84,565)(85,564)(86,563)(87,562)(88,561)(89,560)(90,559)(91,558)(92,557)(93,556)(94,555)(95,554)(96,553)(97,552)(98,551)(99,550)(100,549)(101,548)(102,547)(103,546)(104,545)(105,544)(106,543)(107,542)(108,541)(109,540)(110,539)(111,538)(112,537)(113,536)(114,535)(115,534)(116,533)(117,532)(118,531)(119,530)(120,529)(121,528)(122,527)(123,526)(124,525)(125,524)(126,523)(127,522)(128,521)(129,520)(130,519)(131,518)(132,517)(133,516)(134,515)(135,514)(136,513)(137,512)(138,511)(139,510)(140,509)(141,508)(142,507)(143,506)(144,505)(145,504)(146,503)(147,502)(148,501)(149,500)(150,499)(151,498)(152,497)(153,496)(154,495)(155,494)(156,493)(157,492)(158,491)(159,490)(160,489)(161,488)(162,487)(163,486)(164,485)(165,484)(166,483)(167,482)(168,481)(169,480)(170,479)(171,478)(172,477)(173,476)(174,475)(175,474)(176,473)(177,472)(178,471)(179,470)(180,469)(181,468)(182,467)(183,466)(184,465)(185,464)(186,463)(187,462)(188,461)(189,460)(190,459)(191,458)(192,457)(193,456)(194,455)(195,454)(196,453)(197,452)(198,451)(199,450)(200,449)(201,448)(202,447)(203,446)(204,445)(205,444)(206,443)(207,442)(208,441)(209,440)(210,439)(211,438)(212,437)(213,436)(214,435)(215,434)(216,433)(217,432)(218,431)(219,430)(220,429)(221,428)(222,427)(223,426)(224,425)(225,424)(226,423)(227,422)(228,421)(229,420)(230,419)(231,418)(232,417)(233,416)(234,415)(235,414)(236,413)(237,412)(238,411)(239,410)(240,409)(241,408)(242,407)(243,406)(244,405)(245,404)(246,403)(247,402)(248,401)(249,400)(250,399)(251,398)(252,397)(253,396)(254,395)(255,394)(256,393)(257,392)(258,391)(259,390)(260,389)(261,388)(262,387)(263,386)(264,385)(265,384)(266,383)(267,382)(268,381)(269,380)(270,379)(271,378)(272,377)(273,376)(274,375)(275,374)(276,373)(277,372)(278,371)(279,370)(280,369)(281,368)(282,367)(283,366)(284,365)(285,364)(286,363)(287,362)(288,361)(289,360)(290,359)(291,358)(292,357)(293,356)(294,355)(295,354)(296,353)(297,352)(298,351)(299,350)(300,349)(301,348)(302,347)(303,346)(304,345)(305,344)(306,343)(307,342)(308,341)(309,340)(310,339)(311,338)(312,337)(313,336)(314,335)(315,334)(316,333)(317,332)(318,331)(319,330)(320,329)(321,328)(322,327)(323,326)(324,325)
Polycyclic presentation:
2,3,5,631|b^a=b^2,c^a=c^4,d^a=d^630
Conjugacy classes & character table
4734 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18930, 11);
Finite Group Databasebeta