It is known that the intersection of kernels of all ireducible representations of a finite group in characteristic zero is the trivial group.

In characteristic $p>0$ I have understood that this intersection îs $O_p(G)$, the largest normal $p$ - subgroup of $G$. In other words, all irreducible representations of G are coming from the quotient $G/O_p(G)$.

I have some difficulties in proving this similar result in characteristic $p$ dividing the order of $G$. Could someone provide me with a reference for this result? Or shortly explain the argument to me. My intuition is that this is not so difficult.