Let F be the hyperelliptic genus 2 field given by
y^2 + x*y + x^5 + x.
Using the notation of Magma, let D be the divisor
(x^4 + x + 1, y + x^3 + x^2) +
(x^4 + x + 1, y + x^3 + x^2 + x) + 2*(1/x, y/x^3).
(The first two places in the support of D has degree 4, the last is rational.)
Let S be the set { (x, y), (x + 1, y + x + 1),
(x + 1, y + 1), (x^2 + x + 1)}.
(The first three places in S are rational, the last has degree 4.)
Then F^D_S, the largest abelian extension of F with conductor <=D such that all places in S split completely,
has genus 48 and 35 rational places. This can easily be verified using Magma.