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Dic₅₆₄₉ #36378945

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2,3,7,269,2|a^2=e,b^a=b^2,c^a=c^6,d^a=d^268

Conjugacy classes & character table

5652 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22596, 9);