The unstable N = 42 nucleus 72Zn has been studied using multiple safe Coulomb excitation in inverse kinematics. The experiment was performed at the REX-ISOLDE facility at CERN making first use of the silicon detector array C-REX in combination with the γ -ray spectrometer Miniball. The high angular coverage of C-REX allowed to determine the reduced transition strengths for the decay of the yrast 0+ 1 , 2+ 1 and 4+ 1 as well as of the 0+ 2 and 2+ 2 states in 72Zn. The quadrupole moments of the 2+ 1 , 4+ 1 and 2+ 2 states were extracted. Using model independent quadrupole invariants, the ground state of 72Zn was found to have an average deformation in the γ degree of freedom close to maximum triaxiality. In comparison to experimental data in zinc isotopes with N < 40, the collectivity of the 4+ 1 state in neutron-rich 72Zn is significantly larger, indicating a collective yrast band based on the ground state of 72Zn. In contrast, a low experimental B(E2; 0+ 2 → 2+ 1 ) strength was determined, indicating a different structure for the 0+ 2 state. Shell-model calculations propose a 0+ 2 state featuring a larger fraction of the (spherical) N = 40 closed-shell configuration in its wave function than for the 0+ 1 ground state. The results were also compared with beyond mean field calculations which corroborate the large deformation in the γ degree of freedom, while pointing to a more deformed 0+ 2 state. These experimental and theoretical findings establish the importance of the γ degree of freedom in the ground state of 72Zn, located between the 68,70Ni nuclei that have spherical ground states, and 76Ge, which has a rigid triaxial shape.