Finite Group Databasebeta

?

← Prev (#7626129) Next (#7626131) →

C₂×#34498 #7626130

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

Aliases

Subgroups

8342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533326);