Finite Group Databasebeta

?

← Prev (#354444) Next (#354446) →

C₄×#1860 #354445

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261641);