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C₂×#139427 #72282136

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

Aliases

Subgroups

2327 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 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), (4,8,10,11,9,17,18,16), (3,4)(5,11,13,16)(6,10)(7,9)(8,15,17,12)(14,18), (4,9)(5,12)(6,14)(8,16)(11,17)(13,15));