 Since "q" = "p""n""m" + 1, the order of "GL"2("F""q") = "p"2"n" "m"′.Thus by Theorem 1, the order of the Sylow "p"-subgroups is "p"2"n".One such subgroup "P", is the set of diagonal matrices formula_1, "x" is any primitive root of "F""q".