Finite Group Databasebeta

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D₃×#577 #87205

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 19 points:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19781);