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# of automorphisms of a cyclic group

  1. Sep 11, 2010 #1
    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! ?
  2. jcsd
  3. Sep 11, 2010 #2


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    Try thinking about the automorphisms as mapping the generator of the group to another element
  4. Sep 11, 2010 #3
    Yeah I just realized that once the generator is picked, then the whole group is well defined. So there should be 4 automorphisms?
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