We consider left-invariant (purely) coclosed G\(_2\)-structures on 7-dimensional 2-step nilpotent Lie groups. According to the dimension of the commutator subgroup, we obtain various criteria characterizing the Riemannian metrics induced by left-invariant purely coclosed G\(_2\)-structures. Then, we use them to determine the isomorphism classes of 2-step nilpotent Lie algebras admitting such type of structures. As an intermediate step, we show that every metric on a 2-step nilpotent Lie algebra admitting coclosed G\(_2\)-structures is induced by one of them. Finally, we use our results to give the explicit description of the metrics induced by purely coclosed G\(_2\)-structures on 2-step nilpotent Lie algebras with derived algebra of dimension at most two, up to automorphism.

我们考虑了7维2阶幂等Lie群上的左不变（纯）共封闭G \（_ 2 \）-结构。根据换向器子组的维数，我们获得了表征由左不变纯共封闭G \（_ 2 \）-结构诱导的黎曼度量的各种准则。然后，我们使用它们来确定接纳这种结构类型的两步幂立李代数的同构类。作为中间步骤，我们证明了两步幂幂李代数上允许共封闭G \（_ 2 \）-结构的每个度量都是由其中之一诱发的。最后，我们使用我们的结果对由纯共封闭G \（_ 2 \）引起的度量进行明确描述。-两步幂立李代数上的结构，导出代数的维数最多为2，直至同构。