Finite Group Databasebeta

?

← Prev (#7629789) Next (#7629791) →

C₂×#36155 #7629790

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

Aliases

Subgroups

11264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536986);