  Let $d(G)$ be the minimum number of elements required to generated a group
$G.$ For a group $G $ of order $p^n$ with derived subgroup of order $ p^k $ and
$d(G) = d,$ we knew the order of the Schur multiplier of $G$ is bounded by $
p^{\frac{1}{2}(d-1)(n-k+2)+1}. $ In the current paper, we find the structure of
all $p$-groups that attains the mentioned bound. Moreover, we show that all of
them are capable.
