Finite Group Databasebeta

?

← Prev (#609910) Next (#609912) →

C₂×#15975 #609911

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

Aliases

Subgroups

4962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4,5,6)(11,12,14,15)(13,16,17,18)(19,20,24,26)(21,23,22,25);(8,10)(12,15)(13,17)(19,21,24,22)(20,25,26,23);(7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,22,24,21)(20,25,26,23);(3,4)(5,6)(11,13,14,17)(12,16,15,18)(19,23,24,25)(20,21,26,22)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 517107);