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Let $G$ be a finite group and $\Omega$ a set of $n$ elements. Assume that $G$ acts faithfully on $\Omega$ and let $V$ be a vector space over the complex field $C$, with $\dim V=m\geq 2$. It is shown that for each irreducible constituent $\chi$ of permutation character of $G$, the symmetry class of tensors associated with $G$ and $\chi$ is non-trivial. This extends a result of Merris and Rashid.
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