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D₁₅₈₁₁ #44539416

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

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 260 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);(2,97)(3,96)(4,95)(5,94)(6,93)(7,92)(8,91)(9,90)(10,89)(11,88)(12,87)(13,86)(14,85)(15,84)(16,83)(17,82)(18,81)(19,80)(20,79)(21,78)(22,77)(23,76)(24,75)(25,74)(26,73)(27,72)(28,71)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)(99,260)(100,259)(101,258)(102,257)(103,256)(104,255)(105,254)(106,253)(107,252)(108,251)(109,250)(110,249)(111,248)(112,247)(113,246)(114,245)(115,244)(116,243)(117,242)(118,241)(119,240)(120,239)(121,238)(122,237)(123,236)(124,235)(125,234)(126,233)(127,232)(128,231)(129,230)(130,229)(131,228)(132,227)(133,226)(134,225)(135,224)(136,223)(137,222)(138,221)(139,220)(140,219)(141,218)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,211)(149,210)(150,209)(151,208)(152,207)(153,206)(154,205)(155,204)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,197)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,190)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)(179,180)

Polycyclic presentation:

2,97,163|b^a=b^96,c^a=c^162

Conjugacy classes & character table

7907 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31622, 3);