The normalizer of the level \((2,2)\)-Heisenberg group (Q1802997)

The level \((2,2)\)-Heisenberg group \(G(2,2)\) is a subgroup in \(SL(4,\mathbb{C})\) of order 32. Let \(N\) be its normalizer in \(SL(4,\mathbb{C})\). The author describes explicitly two natural isomorphisms from \(N/G(2,2)\) to the symmetric group \(S_ 6\). The paper was motivated by the author's investigations on certain abelian surfaces.