Finite Group Databasebeta

?

← Prev (#7627751) Next (#7627753) →

C₂×#34597 #7627752

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

Aliases

Subgroups

6556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 7534948);