Finite Group Databasebeta

?

← Prev (#494745) Next (#494747) →

C₂×#13097 #494746

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

Aliases

Subgroups

2016 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401942);