1. The problem statement, all variables and given/known data Find all the automorphisms of a cyclic group of order 10. 2. Relevant equations 3. The attempt at a solution I think it might be useful if I could first figure out how many automorphisms are there. There are 4 elements of order 5, 4 elements of order 10, 1 element of order 1 and 1 element of order 4. So is the # of automorphisms 4!4! ?