Finite Group Databasebeta

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C₂×#13106195 #72226563

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

6418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

(2,3)(4,5)(6,7)(8,9);(1,2,4,5,3)(14,16)(17,18)(19,20);(11,12);(18,20);(7,8)(9,10)(13,14)(15,16)(17,18,19,20)

Conjugacy classes & character table

248 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((2,3)(4,5)(6,7)(8,9), (1,2,4,5,3)(14,16)(17,18)(19,20), (11,12), (18,20), (7,8)(9,10)(13,14)(15,16)(17,18,19,20));