Finite Group Databasebeta

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D₃×#553 #86908

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2,3)(12,14,15,18)(13,17,16,19);(5,9)(8,11)(13,16)(17,19);(4,6,7,10)(5,8,9,11)(13,16)(14,18);(4,5)(6,8)(7,9)(10,11)(12,13)(14,17)(15,16)(18,19);(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, 19484);