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