Finite Group Databasebeta

?

← Prev (#10574050) Next (#10574052) →

C₂²×#2901 #10574051

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

Aliases

Subgroups

22830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481247);