groups which do not have four irreducible characters of degrees divisible by a prime $p$

Given a finite group $g$, we say that $g$ has property $cp_n$ if for every prime integer $p$, $g$ has at most $n-1$ irreducible characters whose degrees are multiples of $p$. ##in this paper, we classify all finite groups that have property $cp_4$. ##we show that the groups satisfying property $cp_4$ are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order $168$, $sl_2(3)$, $alt_5$, $sym_5$, $psl_2(7)$ and $alt_6$.