Task 1 W Let 57 be the group of all permutations of the elements in {1: 2:514:57 6: 7} _ 1 2 3 4 5 6 7 . 1. Given the permutation '7 _ (4 3 7 1 6 5 2) '37' Write o as a product of disjoint bikes. Find the order of o and determines whether 0 is an equal or an odd permutation. 1234567 . 2. Given the permutation ofrom (1) and the permutation T: (\"24653) \"97' Calculate g\"; and 3g. Find the number of elements in the subgroup of 57 that are generated by 0 and t, which means the smallest subgroup of S; that contains a and t. Task 3 Let G be a group of order 323. 1. Show that G has a subgroup of order 19. 2. Let H E G be a subset of G with H at G. Show that H is a cyclic group