Finite Group Databasebeta

?

← Prev (#480366) Next (#480368) →

C₂×#11538 #480367

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

Aliases

Subgroups

912 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 387563);