A finite subgroup of the exceptional Lie group G(2)

With a view to further refining the use of the exceptional group G(2) in at omic and nuclear spectroscopy, it is confirmed that a simple finite subgrou p L-168 similar to PSL2(7) of order 168 of the symmetric group S-8 is also a subgroup of G(2). It is established by character theoretic and other meth ods that there art: two distinct embeddings of L-168 in G(2), analogous to the two distinct embeddings of SO(3) in G(2). Relevant branching rules, ten sor products and symmetrized tensor products are tabulated. As a stimulus t o further applications the branching rules are given for the restriction fr om L-168 to the octahedral crystallographic point group O.