The generalized power of a simple graph G, denoted by Gk,s, is obtained from G by blowing up each vertex into an s-set and each edge into a k-set, where 1≤s≤k2. When s<k2, Gk,s is always odd-bipartite. It is known that Gk,k2 is non-odd-bipartite if and only if G is non-bipartite, and Gk,k2 has the same adjacency (respectively, signless Laplacian) spectral radius as G. In this paper, we prove that, regardless of multiplicities, the H-spectrum of A(Gk,k2) (respectively, Q(Gk,k2)) consists of all eigenvalues of the adjacency matrices (respectively, the signless Laplacian matrices) of the connected induced subgraphs (respectively, modified induced subgraphs) of G. As a corollary, Gk,k2 has the same least adjacency (respectively, least signless Laplacian) H-eigenvalue as G. We also discuss the limit points of the least adjacency H-eigenvalues of hypergraphs, and construct a sequence of non-odd-bipartite hypergraphs whose least adjacency H-eigenvalues converge to −2+5.