Every finite group is the Fitting quotient of a p-dominated group for any prime p not dividing its order
This result was proved in a paper by Hartley and Robinson.
In other words, there is a Finite complete group (?) (i.e., a finite group that is complete: it is centerless and every automorphism is inner) such that the Fitting subgroup (?) is a group of prime power order for the prime , and the quotient group is isomorphic to . In fact, is the semidirect product of and .