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D₃×#541 #86508

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

1004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2,3)(12,15,16,24)(13,18,19,23)(14,22,21,27)(17,25,20,26);(5,9)(8,11)(14,21)(17,20)(22,27)(25,26);(4,6,7,10)(5,8,9,11)(12,14)(13,17)(15,22)(16,21)(18,25)(19,20)(23,26)(24,27);(4,5)(6,8)(7,9)(10,11)(12,13,16,19)(14,20,21,17)(15,23,24,18)(22,25,27,26);(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, 19084);