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The selection of group features is a critical aspect in reducing model complexity by choosing the most essential group features, while eliminating the less significant ones. The existing group feature selection methods select a set of important group features, without providing the relative importance of all group features. Moreover, few methods consider the relative importance of group features in the selection process. This study introduces a permutation-based group feature selection approach specifically designed for high-dimensional multiclass datasets. Initially, the least absolute shrinkage and selection operator (lasso) method was applied to eliminate irrelevant individual features within each group feature. Subsequently, the relative importance of the group features was computed using a random-forest-based permutation method. Accordingly, the process selected the highly significant group features. The performance of the proposed method was evaluated using machine learning algorithms and compared with the performance of other approaches, such as group lasso. We used real-world, high-dimensional, multiclass microarray datasets to demonstrate its effectiveness. The results highlighted the capability of the proposed method, which not only selected significant group features but also provided the relative importance and ranking of all group features. Furthermore, the proposed method outperformed the existing method in terms of accuracy and F1 score.