A 3-local characterization of U6(2) and Fi22

The unitary group U6(2), often referred to as Fi21, and the sporadic simple group Fi22, discovered by Fischer [B. Fischer, Finite groups generated by 3-transpositions. I, Invent. Math. 13 (1971) 232–246 [6]], are characterized by specifying partial information about the structure of the normalizer of a non-trivial 3-central cyclic subgroup.