The power graph Γ G of a finite group G is the graph with the vertex set G , where two distinct elements are adjacent if and only if one is a power of the other. An L (2, 1)-labeling of a graph Γ is an assignment of labels from nonnegative integers to all vertices of Γ such that vertices at distance two get different labels and adjacent vertices get labels that are at least 2 apart. The lambda number of Γ , denoted by λ ( Γ ) , is the minimum span or range over all L (2, 1)-labelings of Γ . In this paper, we obtain bounds for λ ( Γ G ) and give necessary and sufficient conditions when the bounds are attained. As applications, we compute the exact value of λ ( Γ G ) if G is a dihedral group, a generalized quaternion group, a P -group or a cyclic group of order p q n , where p and q are distinct primes and n is a positive integer.