Finite Group Databasebeta

?

← Prev (#7634436) Next (#7634438) →

C₂×#37182 #7634437

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

Aliases

Subgroups

5802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,8)(5,6,10,9)(12,15)(16,18)(19,20,22,23)(21,25,26,24);(4,8)(6,9)(20,23)(24,25);(3,5)(4,9)(6,8)(7,10)(11,12,14,15)(13,16,17,18)(19,20)(21,24)(22,23)(25,26);(3,6,7,9)(4,5,8,10)(19,21)(20,24)(22,26)(23,25);(3,5)(4,9)(6,8)(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, 7541633);