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C₃×#34415 #10653022

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 23 points:

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

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 27403);