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Let {\Lnk} be the class of all $n$-dimensional real solvable Lie algebrashaving $k$-dimensional derived ideals. In 2020 the authors et al. gave aclassification of all non 2-step nilpotent Lie algebras of {\Li}. We propose inthis paper to study representations of these Lie algebras as well as theircorresponding connected and simply connected Lie groups. That is, for eachalgebra, we give an upper bound of the minimal degree of a faithfulrepresentation. Then, we give a geometrical description of coadjoint orbits ofcorresponding groups. Moreover, we show that the characteristic property of thefamily of maximal dimensional coadjoint orbits of a MD-group studied by K. P.Shum and the second author et al. is still true for the Lie groups consideredhere. Namely, we prove that, for each considered group, the family of themaximal dimensional coadjoint orbits forms a measurable foliation in the senseof Connes. The topological classification of these foliations is also provided.

Representation of Real Solvable Lie Algebras Having 2-dimensional Derived Ideal and Geometry of Coadjoint Orbits of Corresponding Lie Groups