Finite Group Databasebeta

?

← Prev (#34843) Next (#34845) →

C₂×#2573 #34844

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

Aliases

Subgroups

1091 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27832);