  We compute the flavorless running coupling constant of QCD from the three
gluon vertex in the (regularisation independent) momentum subtraction
renormalisation scheme. This is performed on the lattice with high statistics.
  The expected color dependence of the Green functions is verified. There are
significant $O(a^2\mu^2)$ effects which can be consistently controlled. Scaling
is demonstrated when the renormalisation scale is varied between 2.1 GeV and
3.85 GeV.
  Scaling when the lattice spacing is varied is very well satisfied. The
resulting flavorless conventional two loop $\Lambda^{(c)}_{\bar{MS}}$ is
estimated to be, respectively for the MOM and $\widetilde{MOM}$ scheme, 361(6)
MeV and 345(6) MeV, while the three loop results are, depending on $\beta_2:
\Lambda^{(3)}_{\bar{MS}} = (412 - 59 \frac{\beta_2} {\beta_{2, \bar{MS}}} \pm 6
MeV) $ and $\Lambda^{(3)}_{\bar{MS}} = (382- 46\frac{\beta_2} {\beta_{2,
\bar{MS}}}\pm 5 MeV) $. A preliminary computation of $\beta_2$ in the
$\widetilde{MOM}$ scheme leads to $\Lambda^{(3)}_{\bar{MS}} = 303(5)\frac
{a^{-1}(\beta=6.0)} {1.97 GeV}$ MeV.
