Recall that the cycle type of an clement of Sn in a sequence

Recall that the cycle type of an clement of S_n in a sequence (l_1, l_r) of cycle lengths such that sum is less than or equal to n. We may assume that cycles are arranged in order of increasing lengths. If here r = 2, and l_1 = 3 the max order is 3.5 = 15 for cycle type (3, 5)

Solution

In an element with r=2 i.e. Total elements are given as 2. And the first element is also given as 3. So the next cycle element can be for length 3 with type (3,5,7) and the maximum order is 105 and so on .