Finite Group Databasebeta

?

← Prev (#7666196) Next (#7666198) →

C₂×#59657 #7666197

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

Aliases

Subgroups

8756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573393);