Finite Group Databasebeta

?

← Prev (#52173) Next (#52175) →

C₂×#2739 #52174

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

Aliases

Subgroups

1035 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45162);