Large automorphism groups of bordered tori

We study large groups of automorphisms of compact orientable bordered Klein surfaces of topological genus one. Here, large means that the order of the group is greater than or equal to 4(g−1), where g≥2 is the algebraic genus of the surface. We find all such groups, providing presentations by means of generators and relations of them. We also determine which of these groups act as the full automorphism group of some bordered torus.