1 for the following questions you may need to look up character tables

Question

1. For the following questions you may need to look-up character tables online. An object has a four-fold principle rotation axis. For the irreducible representationcontaining (x,y) in its linear functions column, use matrices to determine thecharacters in the columns headed by E, C4 and the next listed rotation operation.Also show how matrices can be used to determine the number in front of each ofthe operations i.e. the number of unique operations. Fully explain your reasoning. For the Dsh character table explain the logic used to assign Mulliken symbols to the irreducible representations. You should ignore the subscripts 1 and 2 for the representations but explain all other parts of each Mulliken symbol. Explain the relationship between the symmetry element i, the characters in the column headed by i in character tables and the subscripts g or u that are used in crystal field and molecular orbital energy level diagrams.