Finite Group Databasebeta

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C₃×#60619 #10679226

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2206 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)(13,17)(14,20)(15,22)(18,25)(19,24)(21,26);(5,8)(9,11)(12,13,15,17,16,19,22,24)(14,18,20,23,21,25,26,27);(4,6,7,10)(5,9,8,11)(12,14,15,20,16,21,22,26)(13,18,17,23,19,25,24,27);(14,21)(18,25)(20,26)(23,27);(13,19)(17,24)(18,25)(23,27)

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, 53607);