  We compute the Lens space index for 4d supersymmetric gauge theories
involving symplectic gauge groups. This index can distinguish between different
gauge groups from a given algebra and it matches across theories related by
supersymmetric dualities. We provide explicit calculations for $\mathcal{N}=4$
SYM and for classes of $\mathcal{N}=2$ and $\mathcal{N}=1$ Lagrangian quivers
related by S-duality. In these cases the index matches across the S-dual
phases, while models in different S-duality orbits have a different Lens index.
We provide analogous computations for a 4d $\mathcal{N}=1$ toric quiver gauge
theory corresponding to a $\mathbb{Z}_7$ orbifold of $\mathbb{C}^3$. This
$SU(n)^7$ gauge theory becomes interesting in the case of $n=2$ because it is
conformally dual to other two models, with symplectic and unitary gauge groups,
bifundamentals and antisymmetric tensors. We explicitly check this triality at
the level of the Lens space index.
