Finite Group Databasebeta

?

← Prev (#7634579) Next (#7634581) →

C₂×#37219 #7634580

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

Aliases

Subgroups

5966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541776);