Finite Group Databasebeta

?

← Prev (#7628107) Next (#7628109) →

C₂²×#2563 #7628108

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

Aliases

Subgroups

12234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535304);