Finite Group Databasebeta

?

← Prev (#7628057) Next (#7628059) →

C₂²×#2566 #7628058

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

Aliases

Subgroups

11594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535254);