Finite Group Databasebeta

?

← Prev (#6437617) Next (#6437619) →

C₂×#23904 #6437618

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

Aliases

Subgroups

7300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(10,17)(12,18)(13,20)(19,22);(3,4)(5,6)(7,8,11,14)(9,12,16,18)(10,13,17,20)(15,19,21,22);(4,6)(7,9)(8,12)(10,15)(11,16)(13,19)(14,18)(17,21)(20,22);(7,10)(8,13)(9,15)(11,17)(12,19)(14,20)(16,21)(18,22)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344814);