How to prove Cs is a subgroup of C3v?

[bsmile]

Homework Statement

prove that Cs is a subgroup of C3v group

Homework Equations

The Attempt at a Solution

There are only two elements in Cs group, E and C_sigma. C_sigma is plane reflection operator which does not seem to exist in C3v group. This leads to my question here.

 

[pasmith]

Does C3v contain an element of order 2? If so it has a subgroup isomorphic to Cs.

 

[bsmile]

Does C3v contain an element of order 2? If so it has a subgroup isomorphic to Cs.

Thanks, this makes sense!