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C₂×#649480 #72298536

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

Aliases

Subgroups

93577 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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)(12,14)(16,18), (4,6)(8,9)(15,16)(17,18), (4,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18), (4,6)(8,9)(11,12)(13,14)(15,16)(17,18), (3,4,5,6)(7,9,10,8)(11,12)(13,14)(15,16)(17,18), (1,2));