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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 418 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);(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(23,418)(24,417)(25,416)(26,415)(27,414)(28,413)(29,412)(30,411)(31,410)(32,409)(33,408)(34,407)(35,406)(36,405)(37,404)(38,403)(39,402)(40,401)(41,400)(42,399)(43,398)(44,397)(45,396)(46,395)(47,394)(48,393)(49,392)(50,391)(51,390)(52,389)(53,388)(54,387)(55,386)(56,385)(57,384)(58,383)(59,382)(60,381)(61,380)(62,379)(63,378)(64,377)(65,376)(66,375)(67,374)(68,373)(69,372)(70,371)(71,370)(72,369)(73,368)(74,367)(75,366)(76,365)(77,364)(78,363)(79,362)(80,361)(81,360)(82,359)(83,358)(84,357)(85,356)(86,355)(87,354)(88,353)(89,352)(90,351)(91,350)(92,349)(93,348)(94,347)(95,346)(96,345)(97,344)(98,343)(99,342)(100,341)(101,340)(102,339)(103,338)(104,337)(105,336)(106,335)(107,334)(108,333)(109,332)(110,331)(111,330)(112,329)(113,328)(114,327)(115,326)(116,325)(117,324)(118,323)(119,322)(120,321)(121,320)(122,319)(123,318)(124,317)(125,316)(126,315)(127,314)(128,313)(129,312)(130,311)(131,310)(132,309)(133,308)(134,307)(135,306)(136,305)(137,304)(138,303)(139,302)(140,301)(141,300)(142,299)(143,298)(144,297)(145,296)(146,295)(147,294)(148,293)(149,292)(150,291)(151,290)(152,289)(153,288)(154,287)(155,286)(156,285)(157,284)(158,283)(159,282)(160,281)(161,280)(162,279)(163,278)(164,277)(165,276)(166,275)(167,274)(168,273)(169,272)(170,271)(171,270)(172,269)(173,268)(174,267)(175,266)(176,265)(177,264)(178,263)(179,262)(180,261)(181,260)(182,259)(183,258)(184,257)(185,256)(186,255)(187,254)(188,253)(189,252)(190,251)(191,250)(192,249)(193,248)(194,247)(195,246)(196,245)(197,244)(198,243)(199,242)(200,241)(201,240)(202,239)(203,238)(204,237)(205,236)(206,235)(207,234)(208,233)(209,232)(210,231)(211,230)(212,229)(213,228)(214,227)(215,226)(216,225)(217,224)(218,223)(219,222)(220,221)
Conjugacy classes & character table
7546 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30172, 11);
Finite Group Databasebeta