Projective representation (Z/2Z)^2

Question

I'm not used to projective representations, I guess my question (if well-asked) is trivial.

I have a representation of any $x\in (Z/2Z)^2$ into $U_x\in U_2$ (a complex unitary matrix of dimension 2). I think this is called a projective representation? What can I say, how can I write it?

Thanks

Answer 1

A good answer can be found here, in case someone find this useful: https://groupprops.subwiki.org/wiki/Projective_representation_theory_of_Klein_four-group