  Relative Rota-Baxter groups are generalisations of Rota-Baxter groups and
introduced recently in the context of Lie groups. In this paper, we explore
connections of relative Rota-Baxter groups with skew left braces, which are
well-known to give non-degenerate set-theoretic solutions of the Yang-Baxter
equation. We prove that every relative Rota-Baxter group gives rise to a skew
left brace, and conversely, every skew left brace arises from a relative
Rota-Baxter group. It turns out that there is an isomorphism between the two
categories under some mild restrictions. We propose an efficient GAP algorithm,
which would enable the computation of relative Rota-Baxter operators on finite
groups. In the end, we introduce the notion of isoclinism of relative
Rota-Baxter groups and prove that an isoclinism of these objects induces an
isoclinism of corresponding skew left braces.
