Finite Group Databasebeta

?

← Prev (#7627881) Next (#7627883) →

C₂²×#2477 #7627882

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

Aliases

Subgroups

11610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535078);