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We show that the smallest non‐abelian quotient of    Aut  (   F  n   )    isPSL  n    (  Z  /  2  Z  )   =   L  n    (  2  )    , thus confirming a conjecture of Mecchia–Zimmermann. In the course of the proof we give an exponential (in   n  ) lower bound for the cardinality of a set on which    SAut  (   F  n   )   , the unique index 2 subgroup of    Aut  (   F  n   )   , can act non‐trivially. We also offer new results on the representation theory of    SAut  (   F  n   )    in small dimensions over small, positive characteristics and on rigidity of maps from    SAut  (   F  n   )    to finite groups of Lie type and algebraic groups in characteristic 2.

On the smallest non‐abelian quotient of Aut ( F n )