Suppose G has a cyclic normal subgroup $\langle a\rangle$ of order $m$ and prime power index $s$ such that $m$ and $s$ are relatively prime. Then the following exact sequence splits:
$$1 \longrightarrow \langle a\rangle \longrightarrow G \longrightarrow G/\langle a\rangle \longrightarrow 1$$
Such group G is called a hyperelementary group.
Question: How to define a homomorphism $G/\langle a\rangle \rightarrow G$ to make the above sequence split ?