Finite Group Databasebeta

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D₃×#557 #87030

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

1048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19606);