Finite Group Databasebeta

?

← Prev (#7626015) Next (#7626017) →

C₂×#34406 #7626016

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

Aliases

Subgroups

10634 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)(10,11)(12,14)(15,16)(17,21)(18,22)(19,20);(8,11)(12,13)(16,20)(17,22);(3,5,6,4)(15,17)(16,18)(19,22)(20,21);(7,8)(9,12)(10,11)(13,14)(15,17)(16,18)(19,22)(20,21);(7,9)(8,12)(10,14)(11,13)(15,18)(16,17)(19,21)(20,22)

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, 7533212);