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The method .unit_group() is indeed missing for non-prime finite fields.

Implementing it is the object of

• Sage Trac ticket #7234: Unit groups for finite fields (and more generally)

and that ticket even has a patch with an implementation,

• trac_7234.patch

which one can download and apply to one's installation of Sage.

The ticket has been stalled, but hopefully can be revived.