Chapter 4, Problem 4.22P

Using the ${\text{D}}_{\text{2d}}$ character table,
a. Determine the order of the group.
b. Verify that the E irreducible representation is orthogonal to each of the other irreduciblerepresentations.
c. For each of the irreducible representations, verify that the sum of the squares of thecharacters equals the order of the group.
d. Reduce the following representations to their component irreducible representations: