Finite Group Databasebeta

?

← Prev (#7634435) Next (#7634437) →

C₂×#37172 #7634436

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

Aliases

Subgroups

5672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541632);