Isomorphism relation in $Hom(\mathbb{Z}_6,\mathbb{R}^*\oplus\mathbb{C}^*)?$

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Let $\mathbb{R}^*$ and $\mathbb{C}^*$ are multiplicative group of real number and complex number relatively. what group does isomorphism with $$Hom(\mathbb{Z}_6,\mathbb{R}^*\oplus\mathbb{C}^*)?$$