  After 100 years of effort, the classification of all the finite subgroups of
SU(3) is yet incomplete. The most recently updated list can be found in P.O.
Ludl, J. Phys. A: Math. Theor. 44 255204 (2011), where the structure of the
series (C) and (D) of SU(3)-subgroups is studied. We provide a minimal set of
generators for one of these groups which has order 162. These generators appear
up to phase as the image of an irreducible unitary braid group representation
issued from the Jones-Kauffman version of SU(2) Chern-Simons theory at level 4.
In light of these new generators, we study the structure of the group in detail
and recover the fact that it is isomorphic to the semidirect product Z_9 \times
Z_3 \rtimes S_3 with respect to conjugation.
