Finite Group Databasebeta

?

← Prev (#6431716) Next (#6431718) →

C₂×#23399 #6431717

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

Aliases

Subgroups

7586 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)(9,14)(10,15)(11,19)(12,16)(13,17)(18,21)(20,22);(7,9)(8,13)(10,17)(11,20)(12,18)(14,19)(15,21)(16,22);(4,6)(7,9)(8,14)(10,17)(11,20)(12,18)(13,15)(16,21)(19,22);(7,10,12,11)(8,15,16,19)(9,17,18,20)(13,21,22,14)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338913);