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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 01+, 21+ and 41+ as well as of the 02+ and 22+ states in 72Zn. The quadrupole moments of the 21+, 41+ and 22+ 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 41+ 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;02+→21+) strength was determined, indicating a different structure for the 02+ state. Shell-model calculations propose a 02+ state featuring a larger fraction of the (spherical) N=40 closed-shell configuration in its wave function than for the 01+ 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 02+ 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.