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Aliases
Splittings
Subgroups
60 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 373 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);(4,5)(7,12)(8,11)(9,10)(14,373)(15,372)(16,371)(17,370)(18,369)(19,368)(20,367)(21,366)(22,365)(23,364)(24,363)(25,362)(26,361)(27,360)(28,359)(29,358)(30,357)(31,356)(32,355)(33,354)(34,353)(35,352)(36,351)(37,350)(38,349)(39,348)(40,347)(41,346)(42,345)(43,344)(44,343)(45,342)(46,341)(47,340)(48,339)(49,338)(50,337)(51,336)(52,335)(53,334)(54,333)(55,332)(56,331)(57,330)(58,329)(59,328)(60,327)(61,326)(62,325)(63,324)(64,323)(65,322)(66,321)(67,320)(68,319)(69,318)(70,317)(71,316)(72,315)(73,314)(74,313)(75,312)(76,311)(77,310)(78,309)(79,308)(80,307)(81,306)(82,305)(83,304)(84,303)(85,302)(86,301)(87,300)(88,299)(89,298)(90,297)(91,296)(92,295)(93,294)(94,293)(95,292)(96,291)(97,290)(98,289)(99,288)(100,287)(101,286)(102,285)(103,284)(104,283)(105,282)(106,281)(107,280)(108,279)(109,278)(110,277)(111,276)(112,275)(113,274)(114,273)(115,272)(116,271)(117,270)(118,269)(119,268)(120,267)(121,266)(122,265)(123,264)(124,263)(125,262)(126,261)(127,260)(128,259)(129,258)(130,257)(131,256)(132,255)(133,254)(134,253)(135,252)(136,251)(137,250)(138,249)(139,248)(140,247)(141,246)(142,245)(143,244)(144,243)(145,242)(146,241)(147,240)(148,239)(149,238)(150,237)(151,236)(152,235)(153,234)(154,233)(155,232)(156,231)(157,230)(158,229)(159,228)(160,227)(161,226)(162,225)(163,224)(164,223)(165,222)(166,221)(167,220)(168,219)(169,218)(170,217)(171,216)(172,215)(173,214)(174,213)(175,212)(176,211)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(183,204)(184,203)(185,202)(186,201)(187,200)(188,199)(189,198)(190,197)(191,196)(192,195)(193,194)
Conjugacy classes & character table
7584 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 64);
Finite Group Databasebeta