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Dic₂₇ #1074

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 31 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);(1,3,2,4)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)

Polycyclic presentation:

2^2,3^3|a^2=b,c^3=d^2e,d^3=e^2,c^a=c^2d,d^a=d^2e,e^a=e^2

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(108, 1);