Finite Group Databasebeta

?

← Prev (#60547) Next (#60549) →

C₂×#3119 #60548

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

Aliases

Subgroups

1099 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53536);