Finite Group Databasebeta

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C₃×#14734 #10633341

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

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

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 7722);