Finite Group Databasebeta

?

← Prev (#6348110) Next (#6348112) →

C₂×#18561 #6348111

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

Aliases

Subgroups

3036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255307);