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D8445 #30683290
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 571 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);(2,3)(5,8)(6,7)(10,571)(11,570)(12,569)(13,568)(14,567)(15,566)(16,565)(17,564)(18,563)(19,562)(20,561)(21,560)(22,559)(23,558)(24,557)(25,556)(26,555)(27,554)(28,553)(29,552)(30,551)(31,550)(32,549)(33,548)(34,547)(35,546)(36,545)(37,544)(38,543)(39,542)(40,541)(41,540)(42,539)(43,538)(44,537)(45,536)(46,535)(47,534)(48,533)(49,532)(50,531)(51,530)(52,529)(53,528)(54,527)(55,526)(56,525)(57,524)(58,523)(59,522)(60,521)(61,520)(62,519)(63,518)(64,517)(65,516)(66,515)(67,514)(68,513)(69,512)(70,511)(71,510)(72,509)(73,508)(74,507)(75,506)(76,505)(77,504)(78,503)(79,502)(80,501)(81,500)(82,499)(83,498)(84,497)(85,496)(86,495)(87,494)(88,493)(89,492)(90,491)(91,490)(92,489)(93,488)(94,487)(95,486)(96,485)(97,484)(98,483)(99,482)(100,481)(101,480)(102,479)(103,478)(104,477)(105,476)(106,475)(107,474)(108,473)(109,472)(110,471)(111,470)(112,469)(113,468)(114,467)(115,466)(116,465)(117,464)(118,463)(119,462)(120,461)(121,460)(122,459)(123,458)(124,457)(125,456)(126,455)(127,454)(128,453)(129,452)(130,451)(131,450)(132,449)(133,448)(134,447)(135,446)(136,445)(137,444)(138,443)(139,442)(140,441)(141,440)(142,439)(143,438)(144,437)(145,436)(146,435)(147,434)(148,433)(149,432)(150,431)(151,430)(152,429)(153,428)(154,427)(155,426)(156,425)(157,424)(158,423)(159,422)(160,421)(161,420)(162,419)(163,418)(164,417)(165,416)(166,415)(167,414)(168,413)(169,412)(170,411)(171,410)(172,409)(173,408)(174,407)(175,406)(176,405)(177,404)(178,403)(179,402)(180,401)(181,400)(182,399)(183,398)(184,397)(185,396)(186,395)(187,394)(188,393)(189,392)(190,391)(191,390)(192,389)(193,388)(194,387)(195,386)(196,385)(197,384)(198,383)(199,382)(200,381)(201,380)(202,379)(203,378)(204,377)(205,376)(206,375)(207,374)(208,373)(209,372)(210,371)(211,370)(212,369)(213,368)(214,367)(215,366)(216,365)(217,364)(218,363)(219,362)(220,361)(221,360)(222,359)(223,358)(224,357)(225,356)(226,355)(227,354)(228,353)(229,352)(230,351)(231,350)(232,349)(233,348)(234,347)(235,346)(236,345)(237,344)(238,343)(239,342)(240,341)(241,340)(242,339)(243,338)(244,337)(245,336)(246,335)(247,334)(248,333)(249,332)(250,331)(251,330)(252,329)(253,328)(254,327)(255,326)(256,325)(257,324)(258,323)(259,322)(260,321)(261,320)(262,319)(263,318)(264,317)(265,316)(266,315)(267,314)(268,313)(269,312)(270,311)(271,310)(272,309)(273,308)(274,307)(275,306)(276,305)(277,304)(278,303)(279,302)(280,301)(281,300)(282,299)(283,298)(284,297)(285,296)(286,295)(287,294)(288,293)(289,292)(290,291)
Polycyclic presentation:
2,3,5,563|b^a=b^2,c^a=c^4,d^a=d^562
Conjugacy classes & character table
4224 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16890, 8);
Finite Group Databasebeta