Finite Group Databasebeta

?

← Prev (#10639118) Next (#10639120) →

C₃×#20512 #10639119

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

264 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 13500);