Finite Group Databasebeta

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D₃×#479 #81228

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(9,11,12,18)(10,15,14,23)(13,22,20,19)(16,24,21,17)(25,26,27);(1,3,4,8)(2,5,6,7)(10,14)(15,23)(16,21)(17,24);(1,2,4,6)(3,7,8,5)(9,10,12,14)(11,17,18,24)(13,21,20,16)(15,22,23,19);(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, 13804);