  We present a simple, but efficient, way to calculate connection matrices
between sets of independent local solutions, defined at two neighboring
singular points, of Fuchsian differential equations of quite large orders, such
as those found for the third and fourth contribution ($\chi^{(3)}$ and
$\chi^{(4)}$) to the magnetic susceptibility of square lattice Ising model.
  We use the previous connection matrices to get the exact explicit expressions
of all the monodromy matrices of the Fuchsian differential equation for
$\chi^{(3)}$ (and $\chi^{(4)}$) expressed in the same basis of solutions. These
monodromy matrices are the generators of the differential Galois group of the
Fuchsian differential equations for $\chi^{(3)}$ (and $\chi^{(4)}$), whose
analysis is just sketched here.
