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D₃×#72214299 #72259482

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

3995 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3)(4,5,6)(8,12,13,10,11,15)(9,14)(16,23,19,17,20,21)(18,22);(2,3)(5,6)(7,13,10,9,11,12,14,8,15)(17,18)(19,20)(21,22)(23,24);(5,6)

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2,3)(4,5,6)(8,12,13,10,11,15)(9,14)(16,23,19,17,20,21)(18,22), (2,3)(5,6)(7,13,10,9,11,12,14,8,15)(17,18)(19,20)(21,22)(23,24), (5,6));