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

The outer automorphism group of the Suzuki simple group  ${}^2B_2 (2^{2m+1})$, $m \geq 1$ is cyclic of order $2m+1$ and is generated by a field automorphism $\varphi$ of order $2m+1$. For any almost-simple group $S \leq H \leq {\rm Aut}(S)$ with $S={}^2B_2 (2^{2m+1})$, the group $H/S$ is cyclic. I would like to know

1. the action of $\varphi$ on the conjugacy classes of the group $S$, and

2. the set of complex character degrees of the group $H$.

Thanks for your help.

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

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