  In a recent paper, we defined twisted unitary $1$-groups and showed that they
automatically induced error-detecting quantum codes. We also showed that
twisted unitary $1$-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.
