Is $U(\mathbb{Z}_{54})$ a cyclic group?

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Is the group $U(\mathbb{Z}_{54}) = \{1,5,7,11,13,17,19,23,25,29,31,35,37,41,43,47,49,53\}$ a cyclic group? If so, how do I show this? This group was found as a group of units of the monoid $\mathbb{Z}_{54}$.