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D₂₁₆ #88361

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

Aliases

Splittings

Subgroups

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 35 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);(2,8)(3,7)(4,6)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)

Polycyclic presentation:

2^4,3^3|b^2=cd,c^2=d,e^3=f^2g,f^3=g^2,b^a=bc,c^a=cd,e^a=e^2f,f^a=f^2g,g^a=g^2

Conjugacy classes & character table

111 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 8);