Some sporadic translation planes of order

Abstract

In \cite{PK}, the authors constructed a translation plane of order arising from replacement of a sporadic chain of reguli in a regular spread of . They also showed that two more non isomorphic translation planes, called   and , arise respectively by derivation and double derivation in which correspond to a further replacement of a regulus with its opposite regulus and a pair of reguli with their opposite reguli, respectively.  In \cite{AL}, the authors proved that the translation complement of contains a subgroup isomorphic to . Here, the full collineation group of each of the planes , and is determined.