Finite Group Databasebeta

?

← Prev (#62808) Next (#62810) →

C₂×#3512 #62809

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

Aliases

Subgroups

3619 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55797);