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C₃×#23400 #10642007

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 16388);