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C₃×#60574 #10679181

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 53562);