Finite Group Databasebeta

?

← Prev (#6432685) Next (#6432687) →

C₂×#23837 #6432686

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

Aliases

Subgroups

2210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339882);