Let X be a minimal projecitve complex 3-fold of general type with
canonical Gorenstein singularities and Aut0β(X) be the subgroup of
automorphisms acting trivially on Hβ(X,Q). We prove that if X has
maximal Albanese dimension, β£Aut0β(X)β£β€6. Then we concern the
class of complex varieties X=(C1βΓC2βΓβ―ΓCdβ)/G
(dβ₯2) isogenous to a (higher) product of unmixed type with each
q(Ciβ/G)β₯1. The main result of this paper is that if the irregularity
q(X)β₯d+1, Aut0β(X) is trivial. Moreover, in the case d=3,
let (C1βΓC2βΓC3β)/G itself be the minimal realization of X and
Kiβ be the subgroup of G acting identity on Ciβ, we show that if G is
abelian, every Kiβ is cyclic and q(X)=3, then Aut0β(X)β Z2kβ with k=0,1,2. In the end some examples of complex 3-folds
with Aut0β(X)β Z2β and Z22β are provided