Finite Group Databasebeta

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D₆₅₆ #13050106

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

Aliases

Splittings

Subgroups

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 57 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);(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(18,57)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)

Polycyclic presentation:

2^5,41|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^40,c^b=cd,d^b=de,f^b=f^40

Conjugacy classes & character table

331 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1312, 88);