Finite Group Databasebeta

?

← Prev (#61235) Next (#61237) →

C₂×#3344 #61236

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

Aliases

Subgroups

939 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54224);