In this paper, we determine all homogeneous pseudo-embeddings of the generalized quadrangle H(3, 4) and give a description of all its even sets. Using this description, we subsequently compute all hyperovals of H(3, 4), up to isomorphism, and give computer free descriptions of them. Several of these hyperovals, but not all of them, have already been described before in the literature. (C) 2020 Elsevier Inc. All rights reserved
