Maximal Cofinitary groups are considered close relatives to the maximal almost disjoint families. However, while there are no analytic mad families, there are Borel maximal cofinitary groups. Since every Borel maximal cofinitary group is of size continuum, it is of interest to ask, what the complexities of maximal cofinitary groups of cardinality strictly below the continuum can be. It is known, that in the constructible universe, there are co-analyitc Cohen indestructible maximal cofinitary groups, which gives rise to the existence of a co-analytic maximal cofinitary group of size aleph_1 in a model of large continuum. In this talk, we will discuss the existence of a nicely definable maximal cofinitary group of size strictly between aleph_1 and c (the size of the continuum), which is of minimal projective complexity.