G-Fano threefolds, I

We classify Fano threefolds with only terminal singularities whose canonical class is Cartier and divisible by 2, and satisfying an additional assumption that the $G$-invariant part of the Weil divisor class group is of rank 1 with respect to an action of some group $G$. In particular, we find a lot of examples of Fano 3-folds with "many" symmetries.