p-Parts of character degrees and the index of the Fitting subgroup

In a solvable group G  , if p2p2 does not divide χ(1)χ(1) for all χ∈Irr(G)χ∈Irr(G), then we prove that |G:F(G)|p≤p2|G:F(G)|p≤p2. This bound is best possible.