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We classify compact Riemann surfaces of genus $g$, where $g-1$ is a prime$p$, which have a group of automorphisms of order $\rho(g-1)$ for some integer$\rho\ge 1$, and determine isogeny decompositions of the corresponding Jacobianvarieties. This extends results of Belolipetzky and the second author for$\rho>6$, and of the first and third authors for $\rho=3, 4, 5$ and $6$. As acorollary we classify the orientably regular hypermaps (including maps) ofgenus $p+1$, together with the non-orientable regular hypermaps ofcharacteristic $-p$, with automorphism group of order divisible by the prime$p$; this extends results of Conder, \v Sir\'a\v n and Tucker for maps.

Groups of automorphisms of Riemann surfaces and maps of genus $p+1$ where $p$ is prime