Finite Group Databasebeta

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D₃×#8813 #72225852

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

228 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)(16,17,18,20,19,21,22,23), (8,9,10,12,11,13,14,15), (2,3), (4,5,6,7)(9,12)(10,14)(13,15)(17,20)(18,22)(21,23));