Finite Group Databasebeta

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C₂×#13106268 #72226482

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

5570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

242 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((1,2,4,5,3)(6,7,9,10,8)(13,14,15,16)(17,19,20,18), (2,3)(4,5)(7,8)(9,10)(17,18,20,19), (11,12), (14,16)(18,19), (7,8)(9,10)(18,19));