Finite Group Databasebeta

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C₂×#11714540 #72228366

• solvable
• monomial

Aliases

Splittings

Subgroups

20877 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 14 points:

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

Conjugacy classes & character table

128 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((8,10)(11,12,14), (7,8)(9,10)(12,13), (4,6), (1,2), (3,4)(5,6)(12,13));