Finite Group Databasebeta

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C₃×#21706 #10640313

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 14694);