Finite Group Databasebeta

?

← Prev (#610053) Next (#610055) →

C₂×#16071 #610054

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

Aliases

Subgroups

4594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 517250);