Finite Group Databasebeta

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D₃×#575 #87198

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,4,6,5)(2,9,8,13)(3,11,12,14)(7,16,15,10)(17,18,19);(2,8)(7,15)(9,13)(10,16);(1,3)(2,7)(4,11)(5,14)(6,12)(8,15)(9,16)(10,13);(1,2)(3,10)(4,9)(5,13)(6,8)(7,11)(12,16)(14,15);(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, 19774);