  An algorithm of Thomas Breuer produces complete lists of automorphism groups
of curves for a fixed genus, and the code to execute this algorithm was written
in the computer algebra package GAP and run by Breuer over a decade ago. For
each curve $X$ of genus $g$ and a group $G$ acting on $X$, the branching data
for the covering $X \to X/G$ is computed but was not record. We have added
functionality to the code to output this data, and have translated the code to
the computer algebra package Magma. This article provides an explanation of the
code to add this branching data. Complete data from this modified program for
curves up to genus 20, and data for genus up to 48 of groups $G$ so that
$|G|>4(g-1)$ are available. We also include sample programs which provide a way
to search the data for groups or actions with desired properties, these
functions should be of use to researchers who want to find examples of group
actions on lower genus curves with certain properties, or who need explicit
examples of generating vectors for their research. The code also may be used to
create generating vectors for higher genus curves, if the automorphism group
and signature of the mapping $X \to X/G$ are already know.
