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C₂×#845297 #72267181

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• rational
• ambivalent

Aliases

Subgroups

177385 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

Conjugacy classes & character table

184 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((4,6)(8,10)(12,14), (1,2), (12,14)(16,18), (7,8)(9,10)(15,16)(17,18), (11,12)(13,14)(15,16)(17,18), (3,4)(5,6)(7,8)(9,10));