Some 3-Generator, 3-Relation Finite 2-Groups

Using computational methods, we first show that there are exactly eighteen 3-generator 2-groups of order 2¹⁰ with trivial Schur multiplier all having deficiency zero. We next generalize one of the groups obtained to exhibit two infinite classes of 3-generator, 3-relation finite 2-groups of high nilpotency class providing an affirmative answer to a problem posed by Havas et al.