Finite Group Databasebeta

?

← Prev (#6435416) Next (#6435418) →

C₂×#29690 #6435417

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

Aliases

Subgroups

4610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6342613);