Groups of order 2048 with three generators and three relations

Abstract

It is shown that there are exactly seventy-eight 3-generator‎ ‎2-groups of order $2^{11}$ with trivial Schur multiplier‎. ‎We then‎ ‎give 3-generator‎, ‎3-relation presentations for forty-eight of them‎ ‎proving that these groups have deficiency zero‎.