Let $S^{2}$ denote a sphere of unit radius, centered at the origin of $mathbb{R}^{3}$. What is the

Question:

Let $S^{2}$ denote a sphere of unit radius, centered at the origin of $\mathbb{R}^{3}$. What is the group of transformations that leave it invariant? Next, let $S_{(1)}^{2}$ be a sphere of unit radius, centered at the origin of three-dimensional space, with a point on its surface. What is the group of transformations that leave $S_{(1)}^{2}$ invariant?

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