Derived of Fitting is in Frattini

Verbal statement
The commutator subgroup (or derived subgroup) of the Fitting subgroup of a finite group, is contained in the Frattini subgroup of the whole group.

Statement with symbols
Let $$G$$ be a finite group, and $$F(G)$$, $$\Phi(G)$$ denotes its Fitting subgroup, then $$[F(G),F(G)] \le \Phi(G)$$.

Facts used

 * Primitive implies Fitting-free or elementary Abelian Fitting subgroup