← Prev (#44565698) Next (#44565700) →
Dic8047 #44565699
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 636 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);(1,3,2,4)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(19,636)(20,635)(21,634)(22,633)(23,632)(24,631)(25,630)(26,629)(27,628)(28,627)(29,626)(30,625)(31,624)(32,623)(33,622)(34,621)(35,620)(36,619)(37,618)(38,617)(39,616)(40,615)(41,614)(42,613)(43,612)(44,611)(45,610)(46,609)(47,608)(48,607)(49,606)(50,605)(51,604)(52,603)(53,602)(54,601)(55,600)(56,599)(57,598)(58,597)(59,596)(60,595)(61,594)(62,593)(63,592)(64,591)(65,590)(66,589)(67,588)(68,587)(69,586)(70,585)(71,584)(72,583)(73,582)(74,581)(75,580)(76,579)(77,578)(78,577)(79,576)(80,575)(81,574)(82,573)(83,572)(84,571)(85,570)(86,569)(87,568)(88,567)(89,566)(90,565)(91,564)(92,563)(93,562)(94,561)(95,560)(96,559)(97,558)(98,557)(99,556)(100,555)(101,554)(102,553)(103,552)(104,551)(105,550)(106,549)(107,548)(108,547)(109,546)(110,545)(111,544)(112,543)(113,542)(114,541)(115,540)(116,539)(117,538)(118,537)(119,536)(120,535)(121,534)(122,533)(123,532)(124,531)(125,530)(126,529)(127,528)(128,527)(129,526)(130,525)(131,524)(132,523)(133,522)(134,521)(135,520)(136,519)(137,518)(138,517)(139,516)(140,515)(141,514)(142,513)(143,512)(144,511)(145,510)(146,509)(147,508)(148,507)(149,506)(150,505)(151,504)(152,503)(153,502)(154,501)(155,500)(156,499)(157,498)(158,497)(159,496)(160,495)(161,494)(162,493)(163,492)(164,491)(165,490)(166,489)(167,488)(168,487)(169,486)(170,485)(171,484)(172,483)(173,482)(174,481)(175,480)(176,479)(177,478)(178,477)(179,476)(180,475)(181,474)(182,473)(183,472)(184,471)(185,470)(186,469)(187,468)(188,467)(189,466)(190,465)(191,464)(192,463)(193,462)(194,461)(195,460)(196,459)(197,458)(198,457)(199,456)(200,455)(201,454)(202,453)(203,452)(204,451)(205,450)(206,449)(207,448)(208,447)(209,446)(210,445)(211,444)(212,443)(213,442)(214,441)(215,440)(216,439)(217,438)(218,437)(219,436)(220,435)(221,434)(222,433)(223,432)(224,431)(225,430)(226,429)(227,428)(228,427)(229,426)(230,425)(231,424)(232,423)(233,422)(234,421)(235,420)(236,419)(237,418)(238,417)(239,416)(240,415)(241,414)(242,413)(243,412)(244,411)(245,410)(246,409)(247,408)(248,407)(249,406)(250,405)(251,404)(252,403)(253,402)(254,401)(255,400)(256,399)(257,398)(258,397)(259,396)(260,395)(261,394)(262,393)(263,392)(264,391)(265,390)(266,389)(267,388)(268,387)(269,386)(270,385)(271,384)(272,383)(273,382)(274,381)(275,380)(276,379)(277,378)(278,377)(279,376)(280,375)(281,374)(282,373)(283,372)(284,371)(285,370)(286,369)(287,368)(288,367)(289,366)(290,365)(291,364)(292,363)(293,362)(294,361)(295,360)(296,359)(297,358)(298,357)(299,356)(300,355)(301,354)(302,353)(303,352)(304,351)(305,350)(306,349)(307,348)(308,347)(309,346)(310,345)(311,344)(312,343)(313,342)(314,341)(315,340)(316,339)(317,338)(318,337)(319,336)(320,335)(321,334)(322,333)(323,332)(324,331)(325,330)(326,329)(327,328)
Polycyclic presentation:
2,13,619,2|a^2=d,b^a=b^12,c^a=c^618
Conjugacy classes & character table
8050 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32188, 4);
Finite Group Databasebeta