Finite Group Databasebeta

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D₄×#89101 #72241542

• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

5745 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 14 points:

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

Conjugacy classes & character table

120 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)(5,8,7)(9,10,11)(12,13,14), (10,11)(13,14), (2,4), (2,4)(6,8)(13,14));