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We characterize the unit group of semisimple group algebras FqG of some non-metabelian groups, where Fq is a field with q = p k elements for p prime and a positive integer k. In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group ((C3 × C3)⋊ C3)⋊ C2 of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.

On unit group of finite semisimple group algebras of non-metabelian groups up to order 72