Finite Group Databasebeta

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D₃×#485 #81514

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 14090);