Groups of order ۲۰۴۸ with three generators and three relations

 It is shown that there are exactly seventy-eight ۳-generator‎ ‎۲-groups of order $۲^{۱۱}$ with trivial Schur multiplier‎. ‎We then‎ ‎give ۳-generator‎, ‎۳-relation presentations for forty-eight of them‎ ‎proving that these groups have deficiency zero‎.

Keywords:

Schur multiplier , presentation , deficiency zero , finite $p$-group , lower exponent-$p$ central series