Finite Group Databasebeta

?

← Prev (#6444054) Next (#6444056) →

C₂×#25042 #6444055

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

Aliases

Subgroups

2716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6351251);