Connected Components of ℋ𝐴𝑟,𝑔(𝐺)

The Hurwitz space ℋ𝐴𝑟,𝑔(𝐺) is the space of genus g covers of the Riemann sphere ℙ1 with 𝑟 branch points and the monodromy group 𝐺. In this paper, we enumerate the connected components of the Hurwitz spaces ℋ𝐴𝑟,𝑔(𝐺) for a finite primitive group 𝐺 of degree 7 and genus zero except 𝑆7. We achieve this with the aid of the computer algebra system GAP and the MAPCLASS package.