Recently, interest in bijective functions over finite fields of odd characteristic with good cryptographic properties increased as many cryptographic primitives have been proposed in the literature which operate on prime field \({\mathbb F}_p\) for some large prime p. Here, we consider the boomerang uniformity and the algebraic degree of a class of differentially 4-uniform power permutations over finite fields of odd characteristic. We also determine the compositional inverse of this class of power permutations and compute the algebraic degree of its compositional inverse.