  Stratified groups are those simply connected Lie groups whose Lie algebras
admit a derivation for which the eigenspace with eigenvalue 1 is Lie
generating. When a stratified group is equipped with a left-invariant path
distance that is homogeneous with respect to the automorphisms induced by the
derivation, this metric space is known as Carnot group. Carnot groups appear in
several mathematical contexts. To understand their algebraic structure, it is
useful to study some examples explicitly. In this work, we provide a list of
low-dimensional stratified groups, express their Lie product, and present a
basis of left-invariant vector fields, together with their respective
left-invariant 1-forms, a basis of right-invariant vector fields, and some
other properties. We exhibit all stratified groups in dimension up to 7 and
also study some free-nilpotent groups in dimension up to 14.
