TITLE: Reference request for projective representations of finite groups over a non-problematic field 
QUESTION [11 upvotes]: I would like to get a reference where I can learn about the theory of projective representations of finite groups over the complex numbers (or over any field K such that the order of the given group under study is invertible in K). And how one can relate this to character theory for linear representations (with which I am more familiar). Thanks.

REPLY [2 votes]: In addition: Karpilovsky, Gregory.
The Schur Multiplier. London Math. Soc. Monographs, 1987.
In this book only $\mathbb{C}$ is considered.