Finite Group Databasebeta

?

← Prev (#7629156) Next (#7629158) →

C₂×#35691 #7629157

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

Aliases

Subgroups

16462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536353);