In this paper, we compute the conjugacy classes and the list of irreducible characters of \(\mathrm{GSp}(4,q)\), where \(q\) is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then used to compute dimensions of certain subspaces of fixed vectors of smooth admissible non-supercuspidal representations of \(\mathrm{GSp}(4,F)\), where \(F\) is a non-archimedean local field of characteristic zero with residue field of order \(q\).