Finite Group Databasebeta

?

← Prev (#27189307) Next (#27189309) →

D₆₅₁₃ #27189308

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

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 183 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);(2,3)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(18,183)(19,182)(20,181)(21,180)(22,179)(23,178)(24,177)(25,176)(26,175)(27,174)(28,173)(29,172)(30,171)(31,170)(32,169)(33,168)(34,167)(35,166)(36,165)(37,164)(38,163)(39,162)(40,161)(41,160)(42,159)(43,158)(44,157)(45,156)(46,155)(47,154)(48,153)(49,152)(50,151)(51,150)(52,149)(53,148)(54,147)(55,146)(56,145)(57,144)(58,143)(59,142)(60,141)(61,140)(62,139)(63,138)(64,137)(65,136)(66,135)(67,134)(68,133)(69,132)(70,131)(71,130)(72,129)(73,128)(74,127)(75,126)(76,125)(77,124)(78,123)(79,122)(80,121)(81,120)(82,119)(83,118)(84,117)(85,116)(86,115)(87,114)(88,113)(89,112)(90,111)(91,110)(92,109)(93,108)(94,107)(95,106)(96,105)(97,104)(98,103)(99,102)(100,101)

Polycyclic presentation:

2,3,13,167|b^a=b^2,c^a=c^12,d^a=d^166

Conjugacy classes & character table

3258 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13026, 9);