  We estimate the average group morphological and dynamical characteristics of
the Percolation-Inferred Galaxy Group (2PIGG) catalogue within z~0.08, for
which the group space density is roughly constant. We quantify the different
biases that enter in the determination of these characteristics and we devise
statistical correction procedures to recover their bias free values.
  We find that the only acceptable morphological model is that of prolate, or
triaxial with pronounced prolatness, group shapes having a roughly Gaussian
intrinsic axial ratio distribution with mean ~0.46 and dispersion of ~0.16.
After correcting for various biases, the most important of which is a redshift
dependant bias, the median values of the virial mass and virial radius of
groups with 4 to 30 galaxy members, is: Mv ~6 x 10^12 h_{72}^{-1} M_solar, Rv~
0.4 h^{-1}_{72} Mpc, which are significantly smaller than recent literature
values that do not take into account the previously mentioned biases. The group
mean crossing time is ~1.5 Gyr's, independent of the group galaxy membership.
We also find that there is a correlation of the group size, velocity dispersion
and virial mass with the number of group member galaxies, a manifestation of
the hierarchy of cosmic structures.
