  The study of hidden structures in data presents challenges in modern
statistics and machine learning. We introduce the $\mathbf{gips}$ package in R,
which identifies permutation subgroup symmetries in Gaussian vectors.
$\mathbf{gips}$ serves two main purposes: exploratory analysis in discovering
hidden permutation symmetries and estimating the covariance matrix under
permutation symmetry. It is competitive to canonical methods in dimensionality
reduction while providing a new interpretation of the results. $\mathbf{gips}$
implements a novel Bayesian model selection procedure within Gaussian vectors
invariant under the permutation subgroup introduced in Graczyk, Ishi,
Ko{\l}odziejek, Massam, Annals of Statistics, 50 (3) (2022).
