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We consider the grading of $sl(n,\mathbb{C})$ by the group $\Pi_n$ ofgeneralized Pauli matrices. The grading decomposes the Lie algebra into $n^2-1$one--dimensional subspaces. In the article we demonstrate that the normalizerof grading decomposition of $sl(n,\mathbb{C})$ in $\Pi_n$ is the group $SL(2,\mathbb{Z}_n)$, where $\mathbb{Z}_n$ is the cyclic group of order $n$. As anexample we consider $sl(3,\mathbb{C})$ graded by $\Pi_3$ and all contractionspreserving that grading. We show that the set of 48 quadratic equations forgrading parameters splits into just two orbits of the normalizer of the gradingin $\Pi_3$

Automorphisms of the fine grading of sl(n,C) associated with the generalized Pauli matrices