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C₄×#10591510 #72259885

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

3618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 18 points:

(1,2,3)(4,5,6)(7,8,9,10);(13,18)(15,17);(2,3)(5,6)(12,15,16,17);(5,6)(11,12)(13,15)(14,16)(17,18)

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2,3)(4,5,6)(7,8,9,10), (13,18)(15,17), (2,3)(5,6)(12,15,16,17), (5,6)(11,12)(13,15)(14,16)(17,18));