Finite Group Databasebeta

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D₃×#13049 #72248503

• supersolvable
• solvable
• monomial

Aliases

Splittings

Subgroups

4844 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)(8,16)(10,17)(13,19)(21,22,23);(1,2,4,3)(5,7)(6,10)(8,14,16,20)(9,15)(11,17)(12,13,18,19);(5,6)(7,13,15,19)(8,12)(9,11)(10,14,17,20)(16,18)

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