Title: Mixed Threefolds Isogenous to a Product,
Abstract: In this paper we study \emph{threefolds isogenous to a product of mixed type}
i.e. quotients of a product of three compact Riemann surfaces $C_i$ of genus at
least two by the action of a finite group $G$, which is free, but not diagonal.
In particular, we are interested in the systematic construction and
classification of these varieties. Our main result is the full classification
of threefolds isogenous to a product of mixed type with $\chi(\mathcal O_X)=-1$
assuming that any automorphism in $G$, which restricts to the trivial element
in $Aut(C_i)$ for some $C_i$, is the identity on the product. Since the
holomorphic Euler-Poincaré-characteristic of a smooth threefold of general
type with ample canonical class is always negative, these examples lie on the
boundary, in the sense of threefold geography. To achieve our result we use
techniques from computational group theory. Indeed, we develop a MAGMA
algorithm to classify these threefolds for any given value of $\chi(\mathcal
O_X)$.