Finite Group Databasebeta

?

← Prev (#36652) Next (#36654) →

C₂×#2824 #36653

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

Aliases

Subgroups

1303 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 29641);