= Solution
The <cycle type> records the lengths of the disjoint cycles in a <permutation>, including fixed points as length-one cycles. The possibilities for three objects are
$$
\boxed{\begin{array}{c|c|c}
\text{cycle structure}&\text{elements}&\text{number}\\\hline
1+1+1&e&1\\
2+1&(12),(13),(23)&3\\
3&(123),(132)&2
\end{array}.}
$$
These exhaust the six elements of the <symmetric group> $S_3$, denoted $\Sigma_3$ in the source. They are also the <conjugacy classes of the symmetric group on three letters>.
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