Finite Group Databasebeta

?

← Prev (#7629165) Next (#7629167) →

C₂×#35729 #7629166

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

Aliases

Subgroups

10558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536362);