2, 10.5%) structure of permutation: two permutations have the same structure if they have the same number of cycles of the same length, when written as products of disjoint cycles for example, permutation (12)(345)(67) has the same structure as (13) (245)(67), since they both have two 2-cycles and one 3-cycle; permutation (123) and (123) (4) (5)(6)(7) also have the same structure since in (123), we omit the 1-cycles; (123)(45) and (123)(4)(5) have different structure consider the permutation on 1,2,3,4,5. list the possible structures and their corresponding orders and numbers. the case for 1,2,3,4 is given as an example in table 1 table 1: permutations on (1.2.3.1) ructure order number (12) 6 3 (12)(34)2 3 (1234) 6