Nice Error Bases and Sylow Subgroups

Nice error bases have various applications in quantum computing such as in the teleportation of quantum states and in the theory of noiseless systems. Associated in a natural way to any nice error basis there is a so-called index group and also a group of central type. In this paper, we will extend the number of known index groups for nice error bases by exploiting the connections between groups of central type and their Sylow subgroups. Our methods will allow us find all index groups of degree up to 44 with two exceptions.