Finite Group Databasebeta

?

← Prev (#608609) Next (#608611) →

C₂×#15246 #608610

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

Aliases

Subgroups

4758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 515806);