Finite Group Databasebeta

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D₃×#13050 #72248500

• supersolvable
• solvable
• monomial

Aliases

Splittings

Subgroups

4412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

(22,23);(1,3,4,2)(6,11)(12,19)(13,20)(14,16)(21,22,23);(1,2,4,3)(5,7)(6,10,11,18)(8,16,17,14)(9,15)(12,20)(13,19);(5,6)(7,13,15,20)(8,12)(9,11)(10,14,18,16)(17,19)

Conjugacy classes & character table

102 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((22,23), (1,3,4,2)(6,11)(12,19)(13,20)(14,16)(21,22,23), (1,2,4,3)(5,7)(6,10,11,18)(8,16,17,14)(9,15)(12,20)(13,19), (5,6)(7,13,15,20)(8,12)(9,11)(10,14,18,16)(17,19));