I have been reading a paper which contains the following claim (in the description of Algorithm 6):
If $G$ is a permutation group and and $X_i$ is a non-trivial block-system of $G$, then the block stabilizer ${\rm stab}_G(X_i)$ can be computed in polynomial time (I assume polynomial here means polynomial in $n$ if $G \le S_n$), where ${\rm stab}_G(X_i) = \{g \in G : X_i^g = X_i\}$.
The paper references Holt's Handbook of Computational Group Theory to support this claim which I consulted but I still cannot figure out how this algorithm is supposed to work exactly.
Can someone help me out here?