Finite Group Databasebeta

?

← Prev (#6431972) Next (#6431974) →

C₂²×#2059 #6431973

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

Aliases

Subgroups

4054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

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, 6339169);