The CPT group of the spin-3/2 field

We find out that both the matrix and the operator CPT groups of the spin-3/2 field (with or without mass) are respectively isomorphic to $D_4\rtimes\mathbb{Z}_2$ and $Q\times\mathbb{Z}_2$. These groups are exactly the same groups as for the Dirac field, though there is no a priori reason why they should coincide.Comment: 9 pages. We are replacing the original version (v1) because there was a mistake in the calculation which led to wrong group