This repository contains all left braces of order 64, obtained by Adolfo Ballester-Bolinches, Ramón Esteban-Romero, and Vicent Pérez-Calabuig (additive groups SmallGroup(64, 55) and SmallGroup(64, 192)) and by Valeriy G. Bardakov, Mikhail V. Neshchadim, and Manoj K. Yadav (rest of the additive groups, https://doi.org/10.1142/S0218196720500216). The braces are presented in the form of triply factorised groups.
The tgz archives contain files with names like BRACES64_55/BRACES_199c8_2q5_672.g. This file encodes the information to recover with GAP the skew left braces with additive group SmallGroup(64, 55) and multiplicative group isomorphic to SmallGroup(64, 199) for which the centraliser of action of the multiplicative group on the additive group is isomorphic to SmallGroup(8, 2), the corresponding quotient is isomorphic to SmallGroup(8, 5) (here 8=64/8), and the length of the conjugacy classes of the corresponding regular subgroups in the holomorph is 672.
The trifactorised groups are stored as records that can be read with the function FromRec2Trifact of the trifact2braces.g file. This function admits a record as an argument and returns a group G with G!.K as additive group, G!.C as multiplicative group, and G!.D as diagonal type subgroup. This group can be converted to a skew brace in the sense of hte YangBaxter package for GAP of Konovalov and Vendramin by means of the function FromTrifact2Skewbrace.