We study the weak radiative decays of nucharmed and charmed baryons in the SU(4) and SU(8) symmetry framework. We find that the GIM model of weak interactions gives unsatisfactory results for the weak radiative decays of nucharmed baryons, at SU(4) level. An admixture of 15-dimensional representation of SU(4) in the GIM weak Hamiltonian is indicated. We propose measurement of the decay Ξ- → ∑-γ in order to elucidate the structure of the weak Hamiltonian.