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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 414 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,414)(16,413)(17,412)(18,411)(19,410)(20,409)(21,408)(22,407)(23,406)(24,405)(25,404)(26,403)(27,402)(28,401)(29,400)(30,399)(31,398)(32,397)(33,396)(34,395)(35,394)(36,393)(37,392)(38,391)(39,390)(40,389)(41,388)(42,387)(43,386)(44,385)(45,384)(46,383)(47,382)(48,381)(49,380)(50,379)(51,378)(52,377)(53,376)(54,375)(55,374)(56,373)(57,372)(58,371)(59,370)(60,369)(61,368)(62,367)(63,366)(64,365)(65,364)(66,363)(67,362)(68,361)(69,360)(70,359)(71,358)(72,357)(73,356)(74,355)(75,354)(76,353)(77,352)(78,351)(79,350)(80,349)(81,348)(82,347)(83,346)(84,345)(85,344)(86,343)(87,342)(88,341)(89,340)(90,339)(91,338)(92,337)(93,336)(94,335)(95,334)(96,333)(97,332)(98,331)(99,330)(100,329)(101,328)(102,327)(103,326)(104,325)(105,324)(106,323)(107,322)(108,321)(109,320)(110,319)(111,318)(112,317)(113,316)(114,315)(115,314)(116,313)(117,312)(118,311)(119,310)(120,309)(121,308)(122,307)(123,306)(124,305)(125,304)(126,303)(127,302)(128,301)(129,300)(130,299)(131,298)(132,297)(133,296)(134,295)(135,294)(136,293)(137,292)(138,291)(139,290)(140,289)(141,288)(142,287)(143,286)(144,285)(145,284)(146,283)(147,282)(148,281)(149,280)(150,279)(151,278)(152,277)(153,276)(154,275)(155,274)(156,273)(157,272)(158,271)(159,270)(160,269)(161,268)(162,267)(163,266)(164,265)(165,264)(166,263)(167,262)(168,261)(169,260)(170,259)(171,258)(172,257)(173,256)(174,255)(175,254)(176,253)(177,252)(178,251)(179,250)(180,249)(181,248)(182,247)(183,246)(184,245)(185,244)(186,243)(187,242)(188,241)(189,240)(190,239)(191,238)(192,237)(193,236)(194,235)(195,234)(196,233)(197,232)(198,231)(199,230)(200,229)(201,228)(202,227)(203,226)(204,225)(205,224)(206,223)(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,216)(214,215)
Conjugacy classes & character table
4414 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17644, 9);
Finite Group Databasebeta