Finite Group Databasebeta

?

← Prev (#34089643) Next (#34089645) →

D₉₈₇₂ #34089644

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2^5,617|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^616,c^b=cd,d^b=de,f^b=f^616

Conjugacy classes & character table

4939 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19744, 88);