Finite Group Databasebeta

?

← Prev (#6432321) Next (#6432323) →

C₂×#23712 #6432322

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

Aliases

Subgroups

2748 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339518);