Is there a computer program available to compute Hurwitz numbers easily? In fact I only care about counting covers $C\to\mathbb{P}^1$ branched over $0,1,\infty$, and am even willing to restrict to the case $C=\mathbb{P}^1$.

In combinatorial language, I would like to input integers $d\ge1,g\ge0$ and three partitions $\lambda_1,\lambda_2,\lambda_3$ of $d$ such that the total number of parts of the $\lambda_i$ is $d-2g+2$, and compute, up to simultaneous conjugation, the (weighted) number of permutations $\sigma_1,\sigma_2,\sigma_3\in S_d$, where $\sigma_i$ has cycle type $\lambda_i$, for which the $\sigma_i$ generate a transitive subgroup of $S_d$ and $\sigma_1\sigma_2\sigma_3=1$.


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