Finite Group Databasebeta

?

← Prev (#499392) Next (#499394) →

C₂×#13504 #499393

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

Aliases

Subgroups

684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,11,27,9,14,8,15,10,17,25,33,7,16,26,28)(5,18,23,30,19,12,20,13,21,32,34,29,6,22,24,31);(3,5)(4,12)(6,7)(8,20)(9,19)(10,21)(11,23)(13,27)(14,32)(15,29)(16,18)(17,22)(24,26)(25,34)(28,30)(31,33);(3,6,7,5,10,19,9,21)(4,13,14,30,17,31,16,29)(8,24,11,23,26,20,25,34)(12,28,18,27,22,15,32,33)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406589);