Finite Group Databasebeta

?

← Prev (#6443441) Next (#6443443) →

C₂×#26078 #6443442

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

Aliases

Subgroups

2370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350638);