Finite Group Databasebeta

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D₃×#67×S₄ #72241528

• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

5662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

135 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((2,4)(5,7,8)(9,10,11)(12,13,14), (1,2)(3,4)(6,7)(10,11)(13,14), (6,7), (13,14));