The present manuscript tackles the issue of variable selection for clustering, in high dimensional data described both by numerical and categorical features. First, we build upon the sparse k-means algorithm with lasso penalty, and introduce the group-L1 penalty-already known in regression-in the unsupervised context. Second, we preprocess mixed data and transform categorical features into groups of dummy variables with appropriate scaling, on which one may then apply the group-sparse clustering procedure. The proposed method performs simultaneously clustering and feature selection, and provides meaningful partitions and meaningful features, numerical and categorical, for describing them.