  A group symmetry analysis of the low lying levels of the spin-1/2 kagom\'e
Heisenberg antiferromagnet is performed for small samples up to N=27. This
approach allows to follow the effect of quantum fluctuations when the sample
size increases. The results contradict the scenario of ``order by disorder''
which has been advanced on the basis of large S calculations. A large enough
second neighbor ferromagnetic exchange coupling is needed to stabilize the
$\sqrt 3 \times \sqrt 3$ pattern: the finite size analysis indicates a quantum
critical transition at a non zero coupling.
