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# Full Non-Rigid Group Theory and Symmetry of Melamine

*A.R. Ashrafi*^{1},* and M. Hamadanian^{2}

^{1},* and M. Hamadanian

^{2}

^{1} Department of Chemistry, Faculty of Science, University of Kashan, Kashan, Iran

^{2} Department of Mathematics, Faculty of Science, University of Kashan, Kashan, Iran

The non-rigid molecule group (NRG) theory in which the dynamic symmetry operations are defined as physical operations is a new field in chemistry. Smeyers, in a series of papers, applied this notion to determine the character table of restricted NRG of some molecules. For example, Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG of this molecule is a group of order 648, containing two subgroups of order 324 without inversion [5].

In this work,a simple method is described, through which it is possible to calculate character tables for the symmetry group of molecules. We study the full NRG of melamine, and prove that it is a groups of order 48, with 27 and 10 conjugacy classes. Also, we compute the symmetry of melamine and prove that it is a non-abelian groups of order 6. The method can be generalized to apply to other non-rigid molecules.

**Keywords:** Melamine, Character table, Full non-rigid group, Euclidean matrix