LongestCycleLength on Permutation

The size of the largest cycle (the catalog's second spelling).

On Permutation

Called as CombinatorialStat(x, "LongestCycleLength"). The head's page has its examples.

Live

FindStat St000485

The length of the longest cycle of a permutation.

Object	Value
[1,2]	1
[2,1]	2
[1,2,3]	1
[1,3,2]	2
[2,1,3]	2
[2,3,1]	3
[3,1,2]	3
[3,2,1]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000485 has the rest.