Finite Group Databasebeta

?

← Prev (#7666116) Next (#7666118) →

C₂×#59147 #7666117

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

Aliases

Subgroups

9938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573313);