Finite Group Databasebeta

?

← Prev (#7627988) Next (#7627990) →

C₂²×#2554 #7627989

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

Aliases

Subgroups

11810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535185);