Let $G$ be an odd order nilpotent group with class 2 and $e$ denotes the exponent of its commutator subgroup. Let $e=p_1^{ r_1}p_2^{ r_2}... p_s^{ r_s}$, where $p_i$'s are odd primes and $r_i$'s are non-negative integers. Then there are at least $r_1+r_2+... +r_s$ non-isomorphic nilpotent groups with class two and the order of each of the group is equal to the order of $G$.
Categories: math.GR