Finite Group Databasebeta

?

← Prev (#6448586) Next (#6448588) →

C₂×#24134 #6448587

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

Aliases

Subgroups

3624 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)(9,13)(10,11)(12,14);(8,11)(12,13)(15,16,19,22)(17,23,24,30)(18,26,28,21)(20,27,29,25);(4,6)(15,17,19,24)(16,20,22,29)(18,27,28,25)(21,30,26,23);(7,9,10,14)(8,12,11,13)(17,24)(20,29)(23,30)(25,27)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6355783);