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D₃×#550 #86782

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

1736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 15 points:

(1,2,3)(8,11,12,10)(9,14,13,15);(5,7)(8,10,12,11)(9,14,13,15);(8,9,12,13)(10,14,11,15);(4,5)(6,7)(9,13)(14,15);(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, 19358);