  Given a holomorphic iterated function scheme with a finite symmetry group
$G$, we show that the associated dynamical zeta function factorizes into
symmetry-reduced analytic zeta functions that are parametrized by the unitary
irreducible representations of $G$. We show that this factorization implies a
factorization of the Selberg zeta function on symmetric $n$-funneled surfaces
and that the symmetry factorization simplifies the numerical calculations of
the resonances by several orders of magnitude. As an application this allows us
to provide a detailed study of the spectral gap and we observe for the first
time the existence of a macroscopic spectral gap on Schottky surfaces.
