Finite Group Databasebeta

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C₂×#11761914 #72227476

• non-solvable

Aliases

Subgroups

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

34 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)(3,4,6)(5,7,10)(8,13,14,16,11,18)(9,15,17,20,12,19), (3,11,4,14,6,8)(5,18,12,19,10,13,9,15,7,16,17,20));