No, freedmen were not one of the main social classes in Ancient Greece. In Ancient Greece, the social classes were primarily divided into citizens (free adult male Greeks who enjoyed full rights and privileges), metics (free foreign-born residents in Greek city-states), and slaves (people who were owned by others and had no rights or freedoms). Freedmen were former slaves who had been granted their freedom and could become metics or even citizens in some cases, but they were not a separate social class.
