Understanding C=(2*C5): Elements and Meaning

[chikou24i]

One of the classes of the group C_5v is written C=(2*C₅). So why do we mean by 2*C₅ and how we can know the elements of this class from this writing ?
Thanks

 

[DrDu]

You really mean class or rather symmetry operation? I would guess that 2*C_5 means a rotation by two times 72 degrees.

 

[chikou24i]

I mean what means the notation of the class C'=(2C₅) ,where C' is a class and 2C₅ are the elements of this class.

 

[DrDu]

Where did you see this? I don't think the C' is standard notation. The 2 C$_5$ means that the class contains two elements, namely the rotations by + or - 72 degrees.

 

[chikou24i]

So 2 C₅ means : C₅, C₅⁴.
Thanks you very much that's what I want to know.

 

[DrDu]

Yes, the two are in the same class as e.g. $\sigma_v C_5 \sigma_v=C_5^4$.