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C₂×#3858095 #72297294

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

Aliases

Subgroups

61193 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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((4,5)(16,18), (3,4,6,5)(8,10)(15,16)(17,18), (7,8)(9,10)(12,14), (4,5)(8,10)(11,12)(13,14), (3,5,6,4)(7,8)(9,10), (1,2));