I am having trouble with finding all of the elements of S_4 using cyclic notation.
I know there are 24 elements because 4!=24, but how do I find the elements.
Please help.
Any element is a product of disjoint cycles.
Now find all the different possibilities.
Identity (1): $\displaystyle \text{id}$
2-cycles (6): $\displaystyle (12),(13),(14),(23),(24),(34)$
3-cycles (8): $\displaystyle (123),(124),(132),(134),(142),(143),(234),(243)$
4-cycles (6): $\displaystyle (1234),(1243),(1324),(1342),(1423),(1432)$
2-cycles times 2-cycles (3): $\displaystyle (12)(34),(13)(24),(14)(23)$