  In this paper, we study the properties of the associated gyrogroup
${^\circ}G$ of a given group $G$ of nilpotency class $3$. We have proved that
if $3$ does not divide the order of the group $G$, then the nilpotency class of
the associated gyrogroup ${^\circ}G$ is same as that of the group $G$. We have
also studied the problem of abelian inner mapping group in this context.
