Finite Group Databasebeta

?

← Prev (#6449823) Next (#6449825) →

C₂×#24693 #6449824

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

Aliases

Subgroups

2396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6357020);