Let G be an arbitrary group such that G/Z(G) is finite, where Z(G) denotes the center of the group G. Then γ₂(G), the commutator subgroup of G, is finite. This result is known as Schur's theorem. The converse of this result is not true in general as shown by infinite extra-special p-groups for odd primes. But when G is finitely generated by d elements (say) and γ₂(G) is finite, it was proved by B. H. Neumann that |G/Z(G) | ≤ | γ₂(G) | ^d. In this talk I start with this basic result, discuss a slight generalization and classify all non-abelian finite nilpotent groups G minimally generated by d := d(G) elements such that central quotient is maximal, i.e., |G/Z(G)| = |γ₂(G) | ^d. First I reduce the problem to finite p-groups and then notice that such p-groups admit maximum number of (conjugacy) class-preserving automorphisms. Using this and some basic Lie theoretic techniques, I show that d(G) is even. Moreover, when the nilpotency class of G is at least 3, then d(G) = 2. The situation is then divided into two cases, depending on whether p is even (Magma is extremely useful in this case) or odd, and a complete classification is presented. All p-groups G considered above satisfy the following condition: |x^G| = |γ₂(G)| for all x∈G – Φ(G), where x^G denotes the conjugacy class of x in G and Φ(G) denotes the Frattini subgroup of G. Let me call such a group Camina-type. One of my motives to visit the Computational Algebra group here is to find a solution to the following problem: Does there exist a finite Camina-type p-group G, p odd, of nilpotency class at least 3 such that γ₂(G) < Φ(G) and γ₂(G) is non-cyclic ?