Consider a square where there are points on the four corners and the four midpoints. Find using the cycle index for the group D4.
The identity has 8 cycles of length 1; the three rotations have 2 cycles of length 4; the reflections have 2 cycles of length 1 and 3 cycles of length 2.
Hence, the cycle index is:
But when I expanded this using Wolfram Alpha, I got fractions for some of the coefficients.
I can't seem to find what I did wrong, so I need help finding out.
Thanks in advance.