Representation theory: Examples D8, A4, S4, S5, A5

In this talk we calculate the character tables of several small groups: the dihedral group of order 8, and the alternating and symmetric groups on 4 and 5 points. We do this by first finding the 1-dimensional characters, then finding a few other characters by looking at permutation representations, tensor products, and symmetric and alternating squares, and then finishing by using the orthogonality relations.