Finite Group Databasebeta

?

← Prev (#34768) Next (#34770) →

C₂×#2497 #34769

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

Aliases

Subgroups

1135 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 27757);