TensorSymmetry
TensorSymmetry[tensor] gives the symmetry of tensor under permutations of its slots.
TensorSymmetry[tensor, slots] gives the symmetry under permutation of the specified list of slots.
Examples
Check symmetry of a symmetric matrix:
TensorSymmetry[{{1, 2}, {2, 3}}]
(* Symmetric[{1, 2}] *)Antisymmetric tensor:
TensorSymmetry[{{0, 1}, {-1, 0}}]
(* Antisymmetric[{1, 2}] *)Please visit the official Wolfram Language Reference for more details.