Finite Group Databasebeta

?

← Prev (#7628144) Next (#7628146) →

C₂×#34971 #7628145

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

Aliases

Subgroups

9762 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535341);