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Dic4923 #34089019
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 560 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,560)(16,559)(17,558)(18,557)(19,556)(20,555)(21,554)(22,553)(23,552)(24,551)(25,550)(26,549)(27,548)(28,547)(29,546)(30,545)(31,544)(32,543)(33,542)(34,541)(35,540)(36,539)(37,538)(38,537)(39,536)(40,535)(41,534)(42,533)(43,532)(44,531)(45,530)(46,529)(47,528)(48,527)(49,526)(50,525)(51,524)(52,523)(53,522)(54,521)(55,520)(56,519)(57,518)(58,517)(59,516)(60,515)(61,514)(62,513)(63,512)(64,511)(65,510)(66,509)(67,508)(68,507)(69,506)(70,505)(71,504)(72,503)(73,502)(74,501)(75,500)(76,499)(77,498)(78,497)(79,496)(80,495)(81,494)(82,493)(83,492)(84,491)(85,490)(86,489)(87,488)(88,487)(89,486)(90,485)(91,484)(92,483)(93,482)(94,481)(95,480)(96,479)(97,478)(98,477)(99,476)(100,475)(101,474)(102,473)(103,472)(104,471)(105,470)(106,469)(107,468)(108,467)(109,466)(110,465)(111,464)(112,463)(113,462)(114,461)(115,460)(116,459)(117,458)(118,457)(119,456)(120,455)(121,454)(122,453)(123,452)(124,451)(125,450)(126,449)(127,448)(128,447)(129,446)(130,445)(131,444)(132,443)(133,442)(134,441)(135,440)(136,439)(137,438)(138,437)(139,436)(140,435)(141,434)(142,433)(143,432)(144,431)(145,430)(146,429)(147,428)(148,427)(149,426)(150,425)(151,424)(152,423)(153,422)(154,421)(155,420)(156,419)(157,418)(158,417)(159,416)(160,415)(161,414)(162,413)(163,412)(164,411)(165,410)(166,409)(167,408)(168,407)(169,406)(170,405)(171,404)(172,403)(173,402)(174,401)(175,400)(176,399)(177,398)(178,397)(179,396)(180,395)(181,394)(182,393)(183,392)(184,391)(185,390)(186,389)(187,388)(188,387)(189,386)(190,385)(191,384)(192,383)(193,382)(194,381)(195,380)(196,379)(197,378)(198,377)(199,376)(200,375)(201,374)(202,373)(203,372)(204,371)(205,370)(206,369)(207,368)(208,367)(209,366)(210,365)(211,364)(212,363)(213,362)(214,361)(215,360)(216,359)(217,358)(218,357)(219,356)(220,355)(221,354)(222,353)(223,352)(224,351)(225,350)(226,349)(227,348)(228,347)(229,346)(230,345)(231,344)(232,343)(233,342)(234,341)(235,340)(236,339)(237,338)(238,337)(239,336)(240,335)(241,334)(242,333)(243,332)(244,331)(245,330)(246,329)(247,328)(248,327)(249,326)(250,325)(251,324)(252,323)(253,322)(254,321)(255,320)(256,319)(257,318)(258,317)(259,316)(260,315)(261,314)(262,313)(263,312)(264,311)(265,310)(266,309)(267,308)(268,307)(269,306)(270,305)(271,304)(272,303)(273,302)(274,301)(275,300)(276,299)(277,298)(278,297)(279,296)(280,295)(281,294)(282,293)(283,292)(284,291)(285,290)(286,289)(287,288)
Polycyclic presentation:
2,3,547,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^546,e^a=e^2
Conjugacy classes & character table
4926 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19692, 6);
Finite Group Databasebeta