This paper looks at representing a group G as a group of transformations of an orientable compact bordered Klein surface. We construct visual representations (portraits) of three groups S₄, Z₂ × S₃ and a group L^* of order 32. These groups have real genus 3, 2 and 5 respectively. The first two groups are M^*-groups; which means that they act on surfaces with maximal symmetry. They are also the only solvable M^*-simple groups.