Abstract:We recall the notion of Hopf quasigroups introduced previously by the authors. We construct a bicrossproduct Hopf quasigroup kM
from every group X with a finite subgroup G\subset X and IP quasigroup transversal M\subset X subject to certain conditions. We identify the octonions quasigroup G_{\mathbb O} as transversal in an order 128 group X with subgroup \mathbb Z_2^3 and hence obtain a Hopf quasigroup kG_{\mathbb O}
k(\mathbb Z_2^3) as a particular case of our construction.