Finite Group Databasebeta

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D₈₀₃₃ #30632528

• 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 306 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);(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,306)(32,305)(33,304)(34,303)(35,302)(36,301)(37,300)(38,299)(39,298)(40,297)(41,296)(42,295)(43,294)(44,293)(45,292)(46,291)(47,290)(48,289)(49,288)(50,287)(51,286)(52,285)(53,284)(54,283)(55,282)(56,281)(57,280)(58,279)(59,278)(60,277)(61,276)(62,275)(63,274)(64,273)(65,272)(66,271)(67,270)(68,269)(69,268)(70,267)(71,266)(72,265)(73,264)(74,263)(75,262)(76,261)(77,260)(78,259)(79,258)(80,257)(81,256)(82,255)(83,254)(84,253)(85,252)(86,251)(87,250)(88,249)(89,248)(90,247)(91,246)(92,245)(93,244)(94,243)(95,242)(96,241)(97,240)(98,239)(99,238)(100,237)(101,236)(102,235)(103,234)(104,233)(105,232)(106,231)(107,230)(108,229)(109,228)(110,227)(111,226)(112,225)(113,224)(114,223)(115,222)(116,221)(117,220)(118,219)(119,218)(120,217)(121,216)(122,215)(123,214)(124,213)(125,212)(126,211)(127,210)(128,209)(129,208)(130,207)(131,206)(132,205)(133,204)(134,203)(135,202)(136,201)(137,200)(138,199)(139,198)(140,197)(141,196)(142,195)(143,194)(144,193)(145,192)(146,191)(147,190)(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)(154,183)(155,182)(156,181)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)(163,174)(164,173)(165,172)(166,171)(167,170)(168,169)

Polycyclic presentation:

2,29,277|b^a=b^28,c^a=c^276

Conjugacy classes & character table

4018 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16066, 3);