Abstract: Shape parameters of a weakly deformed ground-state band and highly deformed slightly triaxial sideband in Ca-42 were determined from E2 matrix elements measured in the first low-energy Coulomb excitation experiment performed with AGATA. The picture of two coexisting structures is well reproduced by new state-of-the-art large-scale shell model and beyond-mean-field calculations. Experimental evidence for superdeformation of the band built on 0(2)(+) has been obtained and the role of triaxiality in the A similar to 40 mass region is discussed. Furthermore, the potential of Coulomb excitation as a tool to study superdeformation has been demonstrated for the first time.