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D16075 #44565366
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 668 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);(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(27,668)(28,667)(29,666)(30,665)(31,664)(32,663)(33,662)(34,661)(35,660)(36,659)(37,658)(38,657)(39,656)(40,655)(41,654)(42,653)(43,652)(44,651)(45,650)(46,649)(47,648)(48,647)(49,646)(50,645)(51,644)(52,643)(53,642)(54,641)(55,640)(56,639)(57,638)(58,637)(59,636)(60,635)(61,634)(62,633)(63,632)(64,631)(65,630)(66,629)(67,628)(68,627)(69,626)(70,625)(71,624)(72,623)(73,622)(74,621)(75,620)(76,619)(77,618)(78,617)(79,616)(80,615)(81,614)(82,613)(83,612)(84,611)(85,610)(86,609)(87,608)(88,607)(89,606)(90,605)(91,604)(92,603)(93,602)(94,601)(95,600)(96,599)(97,598)(98,597)(99,596)(100,595)(101,594)(102,593)(103,592)(104,591)(105,590)(106,589)(107,588)(108,587)(109,586)(110,585)(111,584)(112,583)(113,582)(114,581)(115,580)(116,579)(117,578)(118,577)(119,576)(120,575)(121,574)(122,573)(123,572)(124,571)(125,570)(126,569)(127,568)(128,567)(129,566)(130,565)(131,564)(132,563)(133,562)(134,561)(135,560)(136,559)(137,558)(138,557)(139,556)(140,555)(141,554)(142,553)(143,552)(144,551)(145,550)(146,549)(147,548)(148,547)(149,546)(150,545)(151,544)(152,543)(153,542)(154,541)(155,540)(156,539)(157,538)(158,537)(159,536)(160,535)(161,534)(162,533)(163,532)(164,531)(165,530)(166,529)(167,528)(168,527)(169,526)(170,525)(171,524)(172,523)(173,522)(174,521)(175,520)(176,519)(177,518)(178,517)(179,516)(180,515)(181,514)(182,513)(183,512)(184,511)(185,510)(186,509)(187,508)(188,507)(189,506)(190,505)(191,504)(192,503)(193,502)(194,501)(195,500)(196,499)(197,498)(198,497)(199,496)(200,495)(201,494)(202,493)(203,492)(204,491)(205,490)(206,489)(207,488)(208,487)(209,486)(210,485)(211,484)(212,483)(213,482)(214,481)(215,480)(216,479)(217,478)(218,477)(219,476)(220,475)(221,474)(222,473)(223,472)(224,471)(225,470)(226,469)(227,468)(228,467)(229,466)(230,465)(231,464)(232,463)(233,462)(234,461)(235,460)(236,459)(237,458)(238,457)(239,456)(240,455)(241,454)(242,453)(243,452)(244,451)(245,450)(246,449)(247,448)(248,447)(249,446)(250,445)(251,444)(252,443)(253,442)(254,441)(255,440)(256,439)(257,438)(258,437)(259,436)(260,435)(261,434)(262,433)(263,432)(264,431)(265,430)(266,429)(267,428)(268,427)(269,426)(270,425)(271,424)(272,423)(273,422)(274,421)(275,420)(276,419)(277,418)(278,417)(279,416)(280,415)(281,414)(282,413)(283,412)(284,411)(285,410)(286,409)(287,408)(288,407)(289,406)(290,405)(291,404)(292,403)(293,402)(294,401)(295,400)(296,399)(297,398)(298,397)(299,396)(300,395)(301,394)(302,393)(303,392)(304,391)(305,390)(306,389)(307,388)(308,387)(309,386)(310,385)(311,384)(312,383)(313,382)(314,381)(315,380)(316,379)(317,378)(318,377)(319,376)(320,375)(321,374)(322,373)(323,372)(324,371)(325,370)(326,369)(327,368)(328,367)(329,366)(330,365)(331,364)(332,363)(333,362)(334,361)(335,360)(336,359)(337,358)(338,357)(339,356)(340,355)(341,354)(342,353)(343,352)(344,351)(345,350)(346,349)(347,348)
Polycyclic presentation:
2,5,643,5|b^5=d^4,b^a=b^4d,c^a=c^642,d^a=d^4
Conjugacy classes & character table
8039 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32150, 4);
Finite Group Databasebeta