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Among all 2‐(q3+1,q+1,1)‐designs, we characterize the Hermitian unitals by the existence of sufficiently many translations. In arbitrary 2‐(q3+1,q+1,1)‐designs, each group of translations with given center acts semiregularly on the set of points different from the center.

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We give a general construction for unitals of order q admitting an action of SU(2, q). The construction covers the classical hermitian unitals, Grüning's unitals in Hall planes and at least one unital of order four where the translation centers fill precisely one block. For the latter unital, we determine the full group of automorphisms and show that there are no group-preserving embeddings into (dual) translation planes of order 16. Mathematics Subject Classification: 51A10 51E21 05E20