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D₃×#433 #79370

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 27 points:

(1,2,3)(4,6,7,10)(5,9,8,11)(14,20)(17,23)(21,26)(24,27);(5,8)(9,11)(12,14)(13,17)(15,21)(16,20)(18,24)(19,23)(22,26)(25,27);(4,5)(6,9)(7,8)(10,11)(12,13,15,18,16,19,22,25)(14,17,21,24,20,23,26,27);(2,3)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 11946);