Finite Group Databasebeta

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C₂×#3862114 #72294858

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

Aliases

Subgroups

62191 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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