Finite Group Databasebeta

?

← Prev (#7629660) Next (#7629662) →

C₂×#36029 #7629661

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

Aliases

Subgroups

12538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536857);