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In the present paper Lie symmetry group method is applied to find new exact invariant solutions for Klein-Gordon-Fock equation with central symmetry. The found invariant solutions are important for testing finite-difference computational schemes of various boundary value problems of Klein-Gordon-Fock equation with central symmetry. The classical admitted symmetries of the equation are found. The infinitesimal symmetries of the equation are used to find the Riemann function constructively.