Finite Group Databasebeta

?

← Prev (#7629860) Next (#7629862) →

C₂×#36214 #7629861

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

Aliases

Subgroups

15372 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)(13,18)(14,17)(15,16);(7,8,9,10)(11,13)(12,14)(15,17)(16,18);(3,4)(5,6)(12,16)(13,17);(11,12)(13,14)(15,16)(17,18);(11,14)(12,17)(13,16)(15,18)

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, 7537057);