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Dic5057 #35202184
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 406 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);(1,3,2,4)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(19,406)(20,405)(21,404)(22,403)(23,402)(24,401)(25,400)(26,399)(27,398)(28,397)(29,396)(30,395)(31,394)(32,393)(33,392)(34,391)(35,390)(36,389)(37,388)(38,387)(39,386)(40,385)(41,384)(42,383)(43,382)(44,381)(45,380)(46,379)(47,378)(48,377)(49,376)(50,375)(51,374)(52,373)(53,372)(54,371)(55,370)(56,369)(57,368)(58,367)(59,366)(60,365)(61,364)(62,363)(63,362)(64,361)(65,360)(66,359)(67,358)(68,357)(69,356)(70,355)(71,354)(72,353)(73,352)(74,351)(75,350)(76,349)(77,348)(78,347)(79,346)(80,345)(81,344)(82,343)(83,342)(84,341)(85,340)(86,339)(87,338)(88,337)(89,336)(90,335)(91,334)(92,333)(93,332)(94,331)(95,330)(96,329)(97,328)(98,327)(99,326)(100,325)(101,324)(102,323)(103,322)(104,321)(105,320)(106,319)(107,318)(108,317)(109,316)(110,315)(111,314)(112,313)(113,312)(114,311)(115,310)(116,309)(117,308)(118,307)(119,306)(120,305)(121,304)(122,303)(123,302)(124,301)(125,300)(126,299)(127,298)(128,297)(129,296)(130,295)(131,294)(132,293)(133,292)(134,291)(135,290)(136,289)(137,288)(138,287)(139,286)(140,285)(141,284)(142,283)(143,282)(144,281)(145,280)(146,279)(147,278)(148,277)(149,276)(150,275)(151,274)(152,273)(153,272)(154,271)(155,270)(156,269)(157,268)(158,267)(159,266)(160,265)(161,264)(162,263)(163,262)(164,261)(165,260)(166,259)(167,258)(168,257)(169,256)(170,255)(171,254)(172,253)(173,252)(174,251)(175,250)(176,249)(177,248)(178,247)(179,246)(180,245)(181,244)(182,243)(183,242)(184,241)(185,240)(186,239)(187,238)(188,237)(189,236)(190,235)(191,234)(192,233)(193,232)(194,231)(195,230)(196,229)(197,228)(198,227)(199,226)(200,225)(201,224)(202,223)(203,222)(204,221)(205,220)(206,219)(207,218)(208,217)(209,216)(210,215)(211,214)(212,213)
Polycyclic presentation:
2,13,389,2|a^2=d,b^a=b^12,c^a=c^388
Conjugacy classes & character table
5060 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20228, 4);
Finite Group Databasebeta