( cross-posted in Mathematics SE )
 implement a group action in Sage ( for educational purposes )?

Let S= {"A","B","C","D"} and S4= SymmetricGroup(4). I want to create a table of 
the action S4 x S -> S which standardly permutes the letters in the set. The 
table should look like:

Permutation.   A.  B.  C.  D
()             A.  B.  C.  D
(1 2 )         B.  A.  C.  D.
etc.

How can this be done with Sage? ( The Set and Group in the question are just 
examples, I want to be able to create a table for any action.| i

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