In this article, we present a simple agent which learns an internal representation of space without a priori knowledge of its environment, body, or sensors. The learned environment is seen as an internal space representation. This representation is isomorphic to the group of transformations applied to the environment. The model solves certain theoretical and practical issues encountered in previous work in sensorimotor contingency theory. Considering the mathematical description of the internal representation, analysis of its properties and simulations, we prove that this internal representation is equivalent to knowledge of space.