Let ρ be a prime number, ρ ≠ 2, H_p² be a group with the following presentation in the variety of nilpotent groups of class at most two: H_p² = gr(x, y||x^p2 = y^p2 = [x, y]^p = 1) and let qH_p² be the quasivariety generated by the group H_p² . We denote M^p2 = L(qH_p² ), where L(qH_p² ) is the Levi class generated by the quasivariety qH_p². By definition, the Levi class L(qH_p² ) is a class of all groups where the normal closure of every there element belongs to qH_p² . It is well known that the Levi class generated by a quasivariety is a quasivariety too. Besides, the list of quasi-identities that defines the quasivariety M^p2 is known. There is an infinite number of quasi-identities with an arbitrarily large number of variables in the list. The base of the quasivariety is the set of quasi-identities that defines this quasivariety. By the definition, the axiomatic rank of the quasivariety is finite if there is a base of the quasivariety with a finite number of variables. The following question arises: is it true that the axiomatic rank of the quasivariety M^p2 is finite? It is proven that the axiomatic rank of the quasivariety M^p2 is finite, and there is a base of the quasivariety M^p2 that depends on three variables.