Let G be a finite p -group. We show that if Ω2( G ) is an extraspecial group then Ω2( G ) = G . If we assume only that (the subgroup generated by elements of order p 2 ) is an extraspecial group, then the situation is more complicated. If p = 2, then either = G or G is a semidihedral group of order 16. If p > 2, then we can only show that = Hp( G ).