[silimay]

I was reviewing for my final and there is something I don't understand:

Some molecules seem to have more than one principal axis on the same axis.  I don't get it.

For instance, NH3:  I can see how it has a C3 axis.  However, my problem set solutions say it also has something called a C3^2 axis.  How is this possible?  What is that?

[silimay]

Along those same lines, I don't understand why benzene has C3^2 and a C6^5 symmetry elements.

[sjb]

From what I can remember (it's been a while since I did group theory), simply put in the representation of the molecule I've drawn out here, one C₃ axis will map A  B, B  D and D  A, whereas the other will map A D, B  A  and D B .

Does this help?

[silimay]

yeah---that helps a lot.  thanks so much!
-mary-