Exponent conjecture for finite p-groups

Let $G$ be a finite $p$-group, where $p$ is prime. Exponent conjecture for finite $p$-groups.

$$\operatorname{exp}(H_2(G,\mathbb{Z})) \mid p\,\operatorname{exp}(G).$$

This is attributed to the authors of and gives a bound for the exponent of the Schur multiplier of a finite $p$-group. The supplied parser marks the conjecture as refuted; the excerpt does not provide the corresponding counterexample.