Finite Group Databasebeta

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C₃×#60698 #10679305

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1970 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)(14,20)(15,21)(17,23)(19,24)(22,26)(25,27);(5,8)(9,11)(12,13)(14,17)(15,19)(16,18)(20,23)(21,24)(22,25)(26,27);(12,14,21,26,16,22,15,20)(13,17,24,27,18,25,19,23);(4,6,7,10)(5,9,8,11)(14,22)(17,25)(20,26)(23,27);(13,18)(17,25)(19,24)(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, 53686);