How to create a perfectly symmetric mesh?

I have a mesh that is basically the repetition of a mesh unit (first mirrored and then translated). Due to the problem I'm analysing, I have a need for having the mesh sharing the same symmetries as the geometry. Is it possible to create the mesh of the unit in gmsh and then use symmetry (mirror, translation) directly on the mesh unit to enforce that nodes and elements are symmetric as required?

Or is my best choice to just create the unit in gmsh and then use a programming language to do the rest?