Finite Group Databasebeta

?

← Prev (#7629906) Next (#7629908) →

C₂×#36258 #7629907

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

Aliases

Subgroups

14378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537103);