Finite Group Databasebeta

?

← Prev (#7627958) Next (#7627960) →

C₂²×#2500 #7627959

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

Aliases

Subgroups

12130 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)(12,13)(14,16)(17,18,20,22)(19,23,24,21);(10,13)(14,15)(17,18)(19,21)(20,22)(23,24);(5,6,7,8)(9,10)(11,14)(12,13)(15,16);(9,11,12,16)(10,14,13,15)(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, 7535155);