The Picard group Γ = PSL2 (Z(i)) is the group of linear transformations
with a, b, c, d Gaussian integers.
Γ is of interest both as an abstract group and in automorphic function theory [10]. In [10] Waldinger constructed a subgroup H of finite index which is a generalized free product, while in [1] Fine showed that T is a semidirect product with the subgroup H, contained as a subgroup of finite index in the normal factor.