Finite Group Databasebeta

?

← Prev (#7628539) Next (#7628541) →

C₂×#35274 #7628540

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

Aliases

Subgroups

17650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535736);