Finite Group Databasebeta

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D₃×#552 #86858

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

1124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2,3)(14,19)(17,18);(5,9)(8,11)(12,15,16,13)(14,18,19,17);(4,6,7,10)(5,8,9,11)(12,14)(13,17)(15,18)(16,19);(4,5)(6,8)(7,9)(10,11)(12,13,16,15)(14,18,19,17);(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, 19434);