Finite Group Databasebeta

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C₃×#14820 #10633427

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2,3)(5,7)(9,11)(13,15)(16,17,19,21)(18,20,22,23);(12,13,14,15)(18,22)(20,23);(8,9)(10,11)(16,18)(17,20)(19,22)(21,23);(4,5)(6,7)(8,9)(10,11)(16,17)(18,20)(19,21)(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, 7808);