Finite Group Databasebeta

?

← Prev (#7630136) Next (#7630138) →

C₂×#36455 #7630137

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

Aliases

Subgroups

12934 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537333);