= Solution
{c}
The <orbits of a group action> form a <partition of a set> $S$: every element lies in its own <orbit of a group action>, and two intersecting <orbits of a group action> coincide because each point can be moved back and then forward using <inverse elements>. By the <orbit-stabilizer theorem>, each <orbit of a group action> has <cardinality> dividing $8$, so its size is $1,2,4$ or $8$.
If every <orbit of a group action> had size $2,4$ or $8$, their sizes would add to an even number, contrary to $|S|=17$. Therefore there is a one-element <orbit of a group action>, say $\{s'\}$. Every $g\in G$ sends $s'$ into this same singleton, so
$$
\boxed{g\cdot s'=s'\quad\text{for every }g\in G.}
$$
Thus $s'$ is a <fixed point of a group action>. In fact the number of <fixed points of a group action> is odd, since all other <orbits of a group action> have even <cardinality>.
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