Finite Group Databasebeta

?

← Prev (#6446662) Next (#6446664) →

C₂×#25891 #6446663

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

Aliases

Subgroups

6348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6353859);