The Symmetry of Ammonia

Ceulemans, Group Theory Applied to Chemistry, Theoretical Chemistry and Computational Modelling, DOI 10.1007/978-94-007-6863-5 3, 

In this way we can easily work out the full set of binary products, keeping in mind that applying the threefold rotation three times, or the symmetry planes twice, leaves every atom in place and thus corresponds to the unit element. The results are gathered in the 6 x 6 multiplication Table 3.1. This table should be read from left to right, i.e., the product RiRj is found in the /th row and yth column. We may symbolically denote the matrix elements in the table as 

The set of the six matrices in Table 3.2 offers an alternative algebraic way of constructing the multiplication table by direct matrix multiplication. The product C3 i is then replaced by the matrix multiplication D(C3) x D(cri)  

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