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D₃×#563 #87127

• supersolvable
• metabelian
• solvable
• monomial
• stem
• rational
• ambivalent

Aliases

Splittings

Subgroups

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 27 points:

(1,2,3)(5,9)(8,11)(13,19)(14,22)(18,27)(21,23);(5,9)(6,10)(12,15,16,24)(13,18,19,27)(14,21,22,23)(17,25,20,26);(4,6)(5,8)(7,10)(9,11)(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25);(4,5)(6,8)(7,9)(10,11)(12,13,16,19)(14,20,22,17)(15,18,24,27)(21,26,23,25);(2,3)

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19703);