Finite Group Databasebeta

?

← Prev (#6370700) Next (#6370702) →

C₂×#20592 #6370701

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

Aliases

Subgroups

18474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277897);