  Construction of the wave functions of multiquark hadrons by traditional
method based on tensor products of colors, flavors, spins (and orbital) parts
becomes quite complex when quark numbers grow $n=5,6...12$, as it gets
difficult to satisfy requirements of Fermi statistics. Our novel approach is
focused directly on representations of the permutation symmetry generators.
After showing how $C_3$ is manifested in the wave functions of (excited)
baryons, we use it to construct the wave functions for a set of pentaquarks and
hexaquarks (n=5,6). We also have some partial results for larger systems, with
$n=9$ and 12, and even beyond that as far as $n=24$.
