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Following up on my colloquium talk last week I'll get into some details, possibly including: the definition of transfer product (including on the bar construction), examples of how to multiply classes in the cohomology of symmetric groups, a graphical notation for classes, outline of proof(s) of the main calculation, discussion of the divided powers construction (perhaps with a digression into the construction of Steenrod operations), determination of Steenrod algebra action, and some further questions.