Relative stability of geometric magic-number gold nanoclusters with high point-group symmetry (I-h, D-5h, O-h) and size up to 3.5 nm, as well as structures obtained by global optimization using an empirical potential, is investigated using density functional theory (DFT) calculations. Among high-symmetry nanoclusters, our calculations suggest that from Au(147) to Au(923), the stability follows the order I-h > D-5h > O-h. However, at the largest size of Au(923), the computed cohesive energy differences among high-symmetry I-h, D-5h and O-h isomers are less than 4 meV/atom (at PBE level of theory), suggesting the larger high-symmetry clusters are similar in stability. This conclusion supports a recent experimental demonstration of controlling morphologies of high-symmetry Au(923) clusters (Plant, S. R.; Cao, L.; Palmer, R. E. J. Am. Chem. Soc. 2014, 136, 7559). Moreover, at and beyond the size of Au(549), the face-centered cubic-(FCC)-based structure appears to be slightly more stable than the Ih structure with comparable size, consistent with experimental observations. Also, for the Au clusters with the size below or near Au(561), reconstructed icosahedral and decahedral clusters with lower symmetry are slightly more stable than the corresponding high-symmetry isomers. Catalytic activities of both high-symmetry and reconstructed I-h-Au(147) and both I-h-Au(309) clusters are examined. CO adsorption on Au(309) exhibits less sensitivity on the edge and vertex sites compared to Au(147), whereas the CO/O2 coadsorption is still energetically favorable on both gold nanoclusters. Computed activation barriers for CO oxidation are typically around 0.2 eV, suggesting that the gold nanoclusters of similar to 2 nm in size are highly effective catalysts for CO oxidation.