Finite Group Databasebeta

?

← Prev (#7707017) Next (#7707019) →

C₂×#51410 #7707018

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

Aliases

Subgroups

8172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7614214);