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D8411 #30681306
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 660 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,660)(16,659)(17,658)(18,657)(19,656)(20,655)(21,654)(22,653)(23,652)(24,651)(25,650)(26,649)(27,648)(28,647)(29,646)(30,645)(31,644)(32,643)(33,642)(34,641)(35,640)(36,639)(37,638)(38,637)(39,636)(40,635)(41,634)(42,633)(43,632)(44,631)(45,630)(46,629)(47,628)(48,627)(49,626)(50,625)(51,624)(52,623)(53,622)(54,621)(55,620)(56,619)(57,618)(58,617)(59,616)(60,615)(61,614)(62,613)(63,612)(64,611)(65,610)(66,609)(67,608)(68,607)(69,606)(70,605)(71,604)(72,603)(73,602)(74,601)(75,600)(76,599)(77,598)(78,597)(79,596)(80,595)(81,594)(82,593)(83,592)(84,591)(85,590)(86,589)(87,588)(88,587)(89,586)(90,585)(91,584)(92,583)(93,582)(94,581)(95,580)(96,579)(97,578)(98,577)(99,576)(100,575)(101,574)(102,573)(103,572)(104,571)(105,570)(106,569)(107,568)(108,567)(109,566)(110,565)(111,564)(112,563)(113,562)(114,561)(115,560)(116,559)(117,558)(118,557)(119,556)(120,555)(121,554)(122,553)(123,552)(124,551)(125,550)(126,549)(127,548)(128,547)(129,546)(130,545)(131,544)(132,543)(133,542)(134,541)(135,540)(136,539)(137,538)(138,537)(139,536)(140,535)(141,534)(142,533)(143,532)(144,531)(145,530)(146,529)(147,528)(148,527)(149,526)(150,525)(151,524)(152,523)(153,522)(154,521)(155,520)(156,519)(157,518)(158,517)(159,516)(160,515)(161,514)(162,513)(163,512)(164,511)(165,510)(166,509)(167,508)(168,507)(169,506)(170,505)(171,504)(172,503)(173,502)(174,501)(175,500)(176,499)(177,498)(178,497)(179,496)(180,495)(181,494)(182,493)(183,492)(184,491)(185,490)(186,489)(187,488)(188,487)(189,486)(190,485)(191,484)(192,483)(193,482)(194,481)(195,480)(196,479)(197,478)(198,477)(199,476)(200,475)(201,474)(202,473)(203,472)(204,471)(205,470)(206,469)(207,468)(208,467)(209,466)(210,465)(211,464)(212,463)(213,462)(214,461)(215,460)(216,459)(217,458)(218,457)(219,456)(220,455)(221,454)(222,453)(223,452)(224,451)(225,450)(226,449)(227,448)(228,447)(229,446)(230,445)(231,444)(232,443)(233,442)(234,441)(235,440)(236,439)(237,438)(238,437)(239,436)(240,435)(241,434)(242,433)(243,432)(244,431)(245,430)(246,429)(247,428)(248,427)(249,426)(250,425)(251,424)(252,423)(253,422)(254,421)(255,420)(256,419)(257,418)(258,417)(259,416)(260,415)(261,414)(262,413)(263,412)(264,411)(265,410)(266,409)(267,408)(268,407)(269,406)(270,405)(271,404)(272,403)(273,402)(274,401)(275,400)(276,399)(277,398)(278,397)(279,396)(280,395)(281,394)(282,393)(283,392)(284,391)(285,390)(286,389)(287,388)(288,387)(289,386)(290,385)(291,384)(292,383)(293,382)(294,381)(295,380)(296,379)(297,378)(298,377)(299,376)(300,375)(301,374)(302,373)(303,372)(304,371)(305,370)(306,369)(307,368)(308,367)(309,366)(310,365)(311,364)(312,363)(313,362)(314,361)(315,360)(316,359)(317,358)(318,357)(319,356)(320,355)(321,354)(322,353)(323,352)(324,351)(325,350)(326,349)(327,348)(328,347)(329,346)(330,345)(331,344)(332,343)(333,342)(334,341)(335,340)(336,339)(337,338)
Polycyclic presentation:
2,13,647|b^a=b^12,c^a=c^646
Conjugacy classes & character table
4207 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16822, 3);
Finite Group Databasebeta