Is the maximal torus a conjugacy class?

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Let $G$ be a compact Lie group and consider $T$ a maximal torus in $G$.

At Wikipedia I've read that $T$ is a conjugacy class of subgroups of $G$. Does it means that there exist $t \in G$ such that $T = {xtx^{-1}: x \in G}$? Where can I find a proof of this result?

The question above is motivated by this:

If $f$ is an analytic function on $T$ can I extend it to an analytic function on $G$? If the answer of the above question is affirmative, I think it sufices to take the extension of $f$ as $g(x) = f(xtx^{-1})$ for $x \in G$ and $t$ as above.

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What Wikipedia means is that the maximal torus is only well-defined up to conjugacy. A good example worth thinking about in detail is the case $G = U(n)$. You can take $T = U(1)^n$, the diagonal matrices, to be a maximal torus, but "diagonal matrix" implicitly refers to a choice of orthonormal basis of $\mathbb{C}^n$, and so taking a different such basis will result in a different (but conjugate) maximal torus.

The maximal torus is in some sense maximally far from being a single conjugacy class: in fact it intersects every conjugacy class. (For $U(n)$ this follows from the spectral theorem.)