Nontrivial semidirect product of cyclic Lie ring of prime order and cyclic Lie ring of prime-square order

Definition
This Lie ring is defined by the following presentation:

$$\langle a,b \mid p^2a = pb = 0, [a,b] = b \rangle$$

It can also be defined as a semidirect product of Lie rings where the base Lie ring (the ideal) is an abelian Lie ring whose additive group is cyclic of prime order and the acting Lie ring is an abelian Lie ring whose additive group is cyclic of prime-square order, where the derivation induced by the generator of the latter is the identity map.