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I'm currently going through a text about groups, and I'm having problems with composing permutations written in cycle notation, i.e. there are lots of examples and I'm expected to be able to calculate them pretty 'fast', so, is there a way to 'read out' the composition of two permutations direct from the cycle notation (I use standard function composition, which is rather slow), for example, if I have the symmetric group S3, and let's say two of its elements, (2, 3) and (1, 2, 3), how can I figure out what (2, 3) o (1, 2, 3) is? Thanks in advance.