We consider the group formed by finite renormalisations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalisation of the gauge coupling constant, its generators 𝐿𝑛 with n≥1 satisfy the commutation relations of the Witt algebra and therefore form its subalgebra. The commutation relations are also written for the more general case when finite renormalisations are made for both the coupling constant and matter fields. We also construct the generator of the Abelian subgroup corresponding to the changes of the renormalisation scale. The explicit expressions for the renormalisation group generators are written in the case when they act on the β-function and the anomalous dimension. It is explained how the finite changes of these functions under the finite renormalisations can be obtained with the help of the exponential map.