Finite Group Databasebeta

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C₂×#612441 #72323929

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

Aliases

Subgroups

81125 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((16,18), (3,4,6,5)(8,10)(12,14)(16,18), (4,5)(8,10)(11,12)(13,14)(15,16,17,18), (7,8)(9,10), (1,2), (3,5,6,4)(7,8)(9,10));