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D₃×#405 #78547

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 11123);