Why does group action by conjugation on Sylow subgroups define a representation

Question

I am studying representations and I am stumbled upon this:

Take the dicyclic group of order $12: G=\Bbb Z/3\Bbb Z \rtimes \Bbb Z/4\Bbb Z$.

The action of G on its 2-Sylow subgroups appearantly gives a representation of G. I don't understand it. Representation is an action of G on a vector space and $\Bbb Z/4\Bbb Z$ is indeed abelian, so can we view it as a vector space?

Thank you for your help.