Normalizer of a diagonal subgroup of GL2
= Normalizer of a diagonal subgroup of GL2
{title2=$N(T)$}
Over the reals or a <finite field> with more than two elements, the <normalizer> of all invertible diagonal <matrices> in $GL_2$ consists of <monomial matrices> and has quotient $C_2$ over that diagonal <subgroup>. Over $\mathbb F_p$ its size is $2(p-1)^2$ for $p>2$. For $p=2$ the diagonal <subgroup> is trivial, so its normalizer is all of $GL_2(\mathbb F_2)$, of order six.