Finite Group Databasebeta

?

← Prev (#10574192) Next (#10574194) →

C₂²×#2935 #10574193

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

Aliases

Subgroups

11010 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)(9,10,14,17,13,16,22,24)(11,18,20,21,19,15,23,12);(6,8)(9,11)(10,15)(12,17)(13,19)(14,20)(16,18)(21,24)(22,23);(9,12,14,18,13,21,22,15)(10,11,17,20,16,19,24,23);(11,19)(12,21)(15,18)(20,23)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481389);