Finite Group Databasebeta

?

← Prev (#7637091) Next (#7637093) →

C₂×#39167 #7637092

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

Aliases

Subgroups

8686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7544288);