Finite Group Databasebeta

?

← Prev (#6431913) Next (#6431915) →

C₂×#23514 #6431914

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

Aliases

Subgroups

5174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339110);