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C₁₆×Dic₆ #69047

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 27 points:

(1,2,3)(4,6,7,11)(5,8,9,10);(2,3)(4,5,7,9)(6,10,11,8);(12,13,14,17,15,18,20,23,16,19,21,24,22,25,26,27)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 1623);