This article studies a (2+1)-dimensional first extended Calogero-Bogoyavlenskii-Schiff equation, which was recently introduced in the literature. We derive Lie symmetries of this equation and then use them to perform symmetry reductions. Using translation symmetries, a fourth-order ordinary differential equation is obtained which is then solved with the aid of Kudryashov and $ (G'/G)- $expansion techniques to construct closed-form solutions. Besides, we depict the solutions with the appropriate graphical representations. Moreover, conserved vectors of this equation are computed by engaging the multiplier approach as well as Noether's theorem.
Keywords: Kudryashov's method; Lie symmetries; Noether's theorem; conservation laws; extended Calogero-Bogoyavlenskii-Schiff equation.