7. Let o = (15)(26 9 7 8) (34), 7= (1 3 5)(29) € Sg and G=(0,7) < Sg. (a) (7 points) Find the composition a OT, expressed in disjoint cycle

notation. JOT= (b) (7 points) Is a even or odd? Circle the correct answer. EVEN ODD (c) (7 points) Compute the order of a. |o|= (d) (7 points) Considering the action of G on {1,2,3,4,5,6,7,8,9} coming from the inclusion into S9, list the elements of the orbit of G. G.1= (e) (7 points) With the action of G in part (d), we have stabc(1) has 360 elements (you do not need to prove this). What is the order of G? Hint: Use your answer to part (d), even if you couldn't find G.1. |G|=