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This discrete group has three inequivalent one-dimensional representations 

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and one three-dimensional irreducible representation, 3 ; being the Clebsch-Gordan series of their non-trivial products 

In the basis where S is diagonal 

and the decomposition of 3$_{x}$ × 3$_{y}$ reads 

with 3$_{x}$ = ( x$_{1}$, x$_{2}$, x$_{3}$ ) and 3$_{y}$ = ( y$_{1}$, y$_{2}$, y$_{3}$ ). 

## 2. SO (5) generators in the fundamental representation 

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The ten SO (5) generators can be written in the fundamental representation ( 5 ) 

<img src='content_image/350453.jpg'>

