A (finite) quasinilpotent group $G$ is one that satisfies $\mathrm{F}^{\ast}(G)=G$, where $\mathrm{F}^{\ast}$ is the generalised Fitting subgroup of $G$. The class of quasinilpotent groups is a formation (cf. Huppert & Blackburn Finite Groups III p.124), thus every (finite) group has a quasinilpotent residual, i.e. a smallest normal subgroup such that the quotient it affords is quasinilpotent.
My question is: how might one go about constructing the quasinilpotent residual with GAP?