Here are lecture notes, lecture slides, and flashcards for practice with molecular vibrations.
Download and explore an amazing Excel workbook containing 50 character tables; it can be used for reduction of reducible representations. Alternatively, download and try out the program REDUCE. Note: this program requires a dos emulator such as dosemu in order to run; here you can download a howto guide to help you get started.
Examine the IR spectrum of SF6, and also download and read this paper on the SF6 Raman spectrum. Here is an applet for animation/visualization of the SF6 vibrations.
Further Resources: (i) supplemental exercises, (ii) an online reduction operator calculator, and (iii) Daniel Levine's document on Reduction of Reducible Representations.