End ExtremalClass.

(* This is Aschbacher (23.5) *)
Lemma cyclic_SCN gT p (G U : {group gT}) :
p.-group G -> U \in 'SCN(G) -> ~~ abelian G -> cyclic U ->
[/\ p = 2, #|G : U| = 2 & extremal2 G]
\/ exists M : {group gT},
[/\ M :=: 'C_G('Mho^1(U)), #|M : U| = p, extremal_class M = ModularGroup,
'Ohm_1(M)%G \in 'E_p^2(G) & 'Ohm_1(M) \char G].