Finite Group Databasebeta

?

← Prev (#10652354) Next (#10652356) →

C₃×#33748 #10652355

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 27 points:

(1,2,3)(4,5)(6,9)(7,8)(10,11)(13,17)(14,19)(15,21)(18,23)(20,27)(22,26)(24,25);(5,8)(9,11)(13,18)(17,23)(20,24)(25,27);(12,13,19,25,15,20,22,23,16,18,26,27,21,24,14,17);(4,6,7,10)(5,9,8,11)(13,18)(17,23)(20,24)(25,27)

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, 26736);