Left braces of size 8<em>p</em>

Abstract

We describe all left braces of size $8 p$ for an odd prime $p \neq 3,7$ and validate the number given by Bardakov, Neschadim and Yadav in [2]. We give a characterization for isomorphism classes of a semidirect product of left braces and then the description is done by first describing left braces of size 8, as conjuggacy classes of regular subgroups of the corresponding holomorph, and then checking how many non isomorphic left braces of size $8 p$ are obtained from each one of them.