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D₃×#397 #77667

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 19 points:

(1,2,3)(5,7)(9,11)(12,14,15,18)(13,17,16,19);(8,9)(10,11)(13,16)(17,19);(4,5,6,7)(12,13)(14,17)(15,16)(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, 10243);