How to compute the stabilizer subgroup of a partition with GAP?

Question

A partition $P$ of a set $S$ is a set of disjoint subsets of $S$ whose union is $S$. Let $G$ be a subgroup of the symmetric group $S_n$. Define the stabilizer subgroup of $G$ for a partition $P$ of $\{1,2, \dots , n\}$ by $ G_P:= \{g \in G \ | \ gP=P \} $ where $gP:= \{ \{ga \ | \ a \in p \} \ | \ p \in P \}$.

Question: How to compute explicitly $G_P$ with GAP?

Answer 1

Generically it would be a stabilizer

Stabilizer(G,P,OnSetsDisjointSets);

(assuming that $P$ is a set of sets in the GAP sense). IIRC this has been introduced only in recent releases, but the underlying function PartitionStabilizerPermGroup(G,P) has been around for longer. The calculation involves a backtrack search, and probably offers many possibilities for improvement.