id="para0001">This paper is dedicated to a thorough investigation of the symmetries and conservation laws of the geodesic equations associated to a specific exact cosmological solution of a scalar-field potential which was originally motivated by six-dimensional Einstein-Maxwell theory.

id="para0002">The Christoffel symbols and the corresponding system of geodesic equations are computed and then the associated Lie symmetries are totally analyzed.

id="para0003">The algebraic structure of the Lie algebra of local symmetries is briefly investigated and a complete classification of the symmetry subalgebras is presented. Moreover, the corresponding invariant solutions of the system of geodesic equations are discussed.

id="para0005">The Noether symmetries and the Killing vector fields of the geodesic Lagrangian are determined and the corresponding optimal system of one-dimensional subalgebras is constructed.

id="para0006">An entire set of local conservation laws is computed for our analyzed scalar-field cosmological solution.