Finite Group Databasebeta

?

← Prev (#7636830) Next (#7636832) →

C₂×#39464 #7636831

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

Aliases

Subgroups

12792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7544027);