Finite Group Databasebeta

?

← Prev (#6371570) Next (#6371572) →

C₂×#21024 #6371571

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

Aliases

Subgroups

2714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278767);