Finite Group Databasebeta

?

← Prev (#7666974) Next (#7666976) →

C₂×#59815 #7666975

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

Aliases

Subgroups

12446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574171);