High-quality single crystals of trilayer nickelate La₄Ni₃O₁₀ were grown at Sun Yat-Sen University in a HKZ furnace at 20 bar oxygen pressure. The samples were used to determine the atomic structure and perform transport measurements under a pressure of up to 44.3 GPa, as the atomic and electronic structure is fundamental to the understanding superconductivity. A tetragonal structural transition is detected at the same time as the drop in resistance below 7 K occurs. DFT calculations revealed that the structural transition results in a significant change of the Fermi surface, showing an intrinsic connection between the structural symmetry, the electronic band structure and HT_c superconductivity. Together with the recent discovery of superconductivity under pressure in La₄Ni₃O₁₀ from Fudan University, this publication reveals further unique properties of this compound, helping to understand the underlying mechanism of superconductivity in nickelates and high-temperature superconductivity in general.