Finite Group Databasebeta

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D₃×#538 #86413

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

1336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 18989);