Finite Group Databasebeta

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D₈₃₁ #13110324

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem
• Frobenius
• ambivalent

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 280 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);(2,3)(5,280)(6,279)(7,278)(8,277)(9,276)(10,275)(11,274)(12,273)(13,272)(14,271)(15,270)(16,269)(17,268)(18,267)(19,266)(20,265)(21,264)(22,263)(23,262)(24,261)(25,260)(26,259)(27,258)(28,257)(29,256)(30,255)(31,254)(32,253)(33,252)(34,251)(35,250)(36,249)(37,248)(38,247)(39,246)(40,245)(41,244)(42,243)(43,242)(44,241)(45,240)(46,239)(47,238)(48,237)(49,236)(50,235)(51,234)(52,233)(53,232)(54,231)(55,230)(56,229)(57,228)(58,227)(59,226)(60,225)(61,224)(62,223)(63,222)(64,221)(65,220)(66,219)(67,218)(68,217)(69,216)(70,215)(71,214)(72,213)(73,212)(74,211)(75,210)(76,209)(77,208)(78,207)(79,206)(80,205)(81,204)(82,203)(83,202)(84,201)(85,200)(86,199)(87,198)(88,197)(89,196)(90,195)(91,194)(92,193)(93,192)(94,191)(95,190)(96,189)(97,188)(98,187)(99,186)(100,185)(101,184)(102,183)(103,182)(104,181)(105,180)(106,179)(107,178)(108,177)(109,176)(110,175)(111,174)(112,173)(113,172)(114,171)(115,170)(116,169)(117,168)(118,167)(119,166)(120,165)(121,164)(122,163)(123,162)(124,161)(125,160)(126,159)(127,158)(128,157)(129,156)(130,155)(131,154)(132,153)(133,152)(134,151)(135,150)(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)(142,143)

Polycyclic presentation:

2,3,277|b^a=b^2,c^a=c^276

Conjugacy classes & character table

417 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1662, 5);