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Dic4829 #34064569
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 454 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,454)(18,453)(19,452)(20,451)(21,450)(22,449)(23,448)(24,447)(25,446)(26,445)(27,444)(28,443)(29,442)(30,441)(31,440)(32,439)(33,438)(34,437)(35,436)(36,435)(37,434)(38,433)(39,432)(40,431)(41,430)(42,429)(43,428)(44,427)(45,426)(46,425)(47,424)(48,423)(49,422)(50,421)(51,420)(52,419)(53,418)(54,417)(55,416)(56,415)(57,414)(58,413)(59,412)(60,411)(61,410)(62,409)(63,408)(64,407)(65,406)(66,405)(67,404)(68,403)(69,402)(70,401)(71,400)(72,399)(73,398)(74,397)(75,396)(76,395)(77,394)(78,393)(79,392)(80,391)(81,390)(82,389)(83,388)(84,387)(85,386)(86,385)(87,384)(88,383)(89,382)(90,381)(91,380)(92,379)(93,378)(94,377)(95,376)(96,375)(97,374)(98,373)(99,372)(100,371)(101,370)(102,369)(103,368)(104,367)(105,366)(106,365)(107,364)(108,363)(109,362)(110,361)(111,360)(112,359)(113,358)(114,357)(115,356)(116,355)(117,354)(118,353)(119,352)(120,351)(121,350)(122,349)(123,348)(124,347)(125,346)(126,345)(127,344)(128,343)(129,342)(130,341)(131,340)(132,339)(133,338)(134,337)(135,336)(136,335)(137,334)(138,333)(139,332)(140,331)(141,330)(142,329)(143,328)(144,327)(145,326)(146,325)(147,324)(148,323)(149,322)(150,321)(151,320)(152,319)(153,318)(154,317)(155,316)(156,315)(157,314)(158,313)(159,312)(160,311)(161,310)(162,309)(163,308)(164,307)(165,306)(166,305)(167,304)(168,303)(169,302)(170,301)(171,300)(172,299)(173,298)(174,297)(175,296)(176,295)(177,294)(178,293)(179,292)(180,291)(181,290)(182,289)(183,288)(184,287)(185,286)(186,285)(187,284)(188,283)(189,282)(190,281)(191,280)(192,279)(193,278)(194,277)(195,276)(196,275)(197,274)(198,273)(199,272)(200,271)(201,270)(202,269)(203,268)(204,267)(205,266)(206,265)(207,264)(208,263)(209,262)(210,261)(211,260)(212,259)(213,258)(214,257)(215,256)(216,255)(217,254)(218,253)(219,252)(220,251)(221,250)(222,249)(223,248)(224,247)(225,246)(226,245)(227,244)(228,243)(229,242)(230,241)(231,240)(232,239)(233,238)(234,237)(235,236)
Polycyclic presentation:
2,11,439,2|a^2=d,b^a=b^10,c^a=c^438
Conjugacy classes & character table
4832 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19316, 4);
Finite Group Databasebeta