Finite Group Databasebeta

?

← Prev (#52235) Next (#52237) →

C₂×#2792 #52236

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

Aliases

Subgroups

1003 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45224);