Orbits of the actions of finite solvable groups

Suppose V is a completely reducible faithful G-module for a solvable group G, we show G has a “large” orbit on V. Specifically, there is v∈V such that CG(v) is contained in a normal subgroup of derived length 9 contained in the seventh ascending Fitting subgroup of G. This is in some ways best possible. This is applied to generate many theorems showing that a solvable group must have characters of large degree.