Finite Group Databasebeta

?

← Prev (#7622916) Next (#7622918) →

C₂²×#2210 #7622917

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

Aliases

Subgroups

2366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530113);