Abstract
In a recent paper, we defined twisted unitary -groups and showed that they automatically induced error-detecting quantum codes. We also showed that twisted unitary -groups correspond to irreducible products of characters thereby reducing the problem of code-finding to a computation in the character theory of finite groups. Using a combination of GAP computations and results from the mathematics literature on irreducible products of characters, we identify many new non-trivial quantum codes with unusual transversal gates.