Hi, I know that over $\mathbb{C}$ the dimension of an irreducible representation of a finite group $G$ must divide the order of the group. I've read somewhere that if $p$ does not divide the order of the group then the representations over $\tilde{F_p}$ are "essentially the same" (Is this true? What does it mean other than the dimensions are of the same size and number?)

My question is if anything can be said in general about the dimesions of the irreducible representations when $p$ does divide $|G|$? Can anything be said about dimensions of faithful irreducible representations (if such exist)?

Also, can someone recomend a good "friendly" (I am from computer science dept.) refrence for such statements?

Thanks