The Outer automorphism group of the Suzuki simple group 2B_2 (2^(2m+1)), m>=1 is cyclic of order 2m+1 and is generated by a field automorphism ϕ of order 2m+1. For any almost simple group S≤H≤Aut(s) with S=^2B_2 (2^(2m+1)), the group H/S is cyclic. Due to this, I want to know 1) The action of ϕ on the conjugacy classes of the group S , and so 2) the set of complex character degrees of the group H? Thanks for your help