University of Isfahan International Journal of Group Theory 2251-7650 1 1 2012 03 01 Groups of order 2048 with three generators and three relations 29 37 470 10.22108/ijgt.2012.470 EN S. Fouladi R. Orfi Journal Article 2011 07 27  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. Schur multiplier presentation deficiency zero finite $p$-group lower exponent-$p$ central series https://ijgt.ui.ac.ir/article_470_fcd7ddcb5b52b3c1b3764203d5e9bab6.pdf