Finite Group Databasebeta

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C₃×#15669 #10634276

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1934 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 27 points:

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

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, 8657);