  The strong symmetric genus of a finite group is the minimum genus of a
compact Riemann surface on which the group acts as a group of automorphisms
preserving orientation. A characterization of the infinite number of groups
with strong symmetric genus zero and one is well-known and the problem is
finite for each strong symmetric genus greater than or equal to two. May and
Zimmerman have published papers detailing the classification of all groups with
strong symmetric genus two through four. Using the computer algebra system GAP,
we extend these classifications to all groups of strong symmetric genus up to
twenty-five. This paper outlines the approach used for the extension.
