The realization of center and chiral symmetries in N = 1 super Yang-Mills theory (SYM) is investigated on a four-dimensional Euclidean lattice by means of Monte Carlo methods. At zero temperature this theory is expected to confine external fundamental charges and to have a nonvanishing gaugino condensate, which breaks the nonanomalous Z(2Nc) chiral symmetry. In this work we find, for the first time, a nonvanishing condensate at zero temperature and zero gaugino mass with Wilson fermions. This is achieved by means of the renormalization properties of the Yang-Mills and fermion gradient flows, which are independent of the lattice regularization. At finite temperatures, we find that the phase transitions corresponding to deconfinement and chiral restoration occur at roughly the same critical temperature for SU(2) gauge group, implying the saturation of the bound T-c(hiral)c <= T-d(ec)c, recently obtained through anomaly matching. We furthermore discuss the agreement of our findings with conjectures from superstring theory.