Finite Group Databasebeta

?

← Prev (#6431953) Next (#6431955) →

C₂×#23544 #6431954

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

Aliases

Subgroups

5466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,6)(11,12)(13,21)(14,17)(15,20)(16,19)(18,22)(23,25)(24,26);(7,8)(9,10)(12,17)(13,22)(14,15)(18,25)(19,20)(23,24);(4,6)(8,10)(11,13,14,23,16,24,15,22)(12,18,20,26,19,25,17,21);(12,19)(17,20)(18,25)(21,26)

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, 6339150);