Finite Group Databasebeta

?

← Prev (#6443631) Next (#6443633) →

C₂×#26978 #6443632

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

Aliases

Subgroups

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350828);