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Stratified groups are those simply connected Lie groups whose Lie algebrasadmit a derivation for which the eigenspace with eigenvalue 1 is Liegenerating. When a stratified group is equipped with a left-invariant pathdistance that is homogeneous with respect to the automorphisms induced by thederivation, this metric space is known as Carnot group. Carnot groups appear inseveral mathematical contexts. To understand their algebraic structure, it isuseful to study some examples explicitly. In this work, we provide a list oflow-dimensional stratified groups, express their Lie product, and present abasis of left-invariant vector fields, together with their respectiveleft-invariant 1-forms, a basis of right-invariant vector fields, and someother properties. We exhibit all stratified groups in dimension up to 7 andalso study some free-nilpotent groups in dimension up to 14.

A Cornucopia of Carnot groups in Low Dimensions