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Dic5943 #37557775
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 297 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);(1,3,2,4)(6,7)(9,14)(10,13)(11,12)(16,297)(17,296)(18,295)(19,294)(20,293)(21,292)(22,291)(23,290)(24,289)(25,288)(26,287)(27,286)(28,285)(29,284)(30,283)(31,282)(32,281)(33,280)(34,279)(35,278)(36,277)(37,276)(38,275)(39,274)(40,273)(41,272)(42,271)(43,270)(44,269)(45,268)(46,267)(47,266)(48,265)(49,264)(50,263)(51,262)(52,261)(53,260)(54,259)(55,258)(56,257)(57,256)(58,255)(59,254)(60,253)(61,252)(62,251)(63,250)(64,249)(65,248)(66,247)(67,246)(68,245)(69,244)(70,243)(71,242)(72,241)(73,240)(74,239)(75,238)(76,237)(77,236)(78,235)(79,234)(80,233)(81,232)(82,231)(83,230)(84,229)(85,228)(86,227)(87,226)(88,225)(89,224)(90,223)(91,222)(92,221)(93,220)(94,219)(95,218)(96,217)(97,216)(98,215)(99,214)(100,213)(101,212)(102,211)(103,210)(104,209)(105,208)(106,207)(107,206)(108,205)(109,204)(110,203)(111,202)(112,201)(113,200)(114,199)(115,198)(116,197)(117,196)(118,195)(119,194)(120,193)(121,192)(122,191)(123,190)(124,189)(125,188)(126,187)(127,186)(128,185)(129,184)(130,183)(131,182)(132,181)(133,180)(134,179)(135,178)(136,177)(137,176)(138,175)(139,174)(140,173)(141,172)(142,171)(143,170)(144,169)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)(152,161)(153,160)(154,159)(155,158)(156,157)
Polycyclic presentation:
2,3,7,283,2|a^2=e,b^a=b^2,c^a=c^6,d^a=d^282
Conjugacy classes & character table
5946 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23772, 12);
Finite Group Databasebeta