Finite Group Databasebeta

?

← Prev (#10679664) Next (#10679666) →

C₃×#61058 #10679665

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 54046);