In this paper, we derive an asymptotic formula for the number of conjugacy classes of elements in a class of statistically convex-cocompact actions with contracting elements. Denote by $\mathcal C(n)$ (resp. $\mathcal C'(n)$) the set of (resp. primitive) conjugacy classes of stable length at most $n$. The main result is an asymptotic formula as follows: $$\sharp \mathcal C(n) \asymp \sharp \mathcal C'(n) \asymp \frac{\exp(\e G)}{n}.$$ The same formula holds for conjugacy classes using pointed length for any given basepoint. As a consequence of the formulae, the conjugacy growth series is transcendental for all non-elementary relatively hyperbolic groups, graphical small cancellation groups with finite components. As by-product of the proof, we establish several useful properties for an exponentially generic set of elements. In particular, it yields a positive answer to a question of Maher that an exponentially generic elements in mapping class groups have their Teichm\"{u}ller axis con 查看全文>>