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We consider all connected and simply connected 7-dimensional Lie groups whoseLie algebras have nilradical $\g_{5,2} = \s \{X_1, X_2, X_3, X_4, X_5 \colon[X_1, X_2] = X_4, [X_1, X_3] = X_5\}$ of Dixmier. First, we give a geometricdescription of the maximal-dimensional orbits in the coadjoint representationof all considered Lie groups. Next, we prove that, for each considered group,the family of the generic coadjoint orbits forms a measurable foliation in thesense of Connes. Finally, the topological classification of all thesefoliations is also provided.

Foliations Formed by Generic Coadjoint Orbits of Lie Groups Corresponding to a Class Seven-Dimensional Solvable Lie Algebras