Finite Group Databasebeta

?

← Prev (#60792) Next (#60794) →

C₂×#3224 #60793

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

Aliases

Subgroups

1139 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53781);