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Is there a nice reference where I can get the information of $H^*(BG)$ with coefficients in $\mathbb{Z}$ or $\mathbb{Z}/p\mathbb{Z}$, with $G$ not just $SO$ or $U$ but for example $G=PSU(n)$, $Pin(n)$, $SO(2n)/\{\pm 1\}$, or $Aut(E_6)$?

I'm happy if I could get the info on the structure of the cohomology up to the degree 4 (as a 4d gauge theorist) or to the degree 10 (as a string theorist.)

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    $\begingroup$ Have a Look at Mimura-Toda "Topology of Lie Groups" or Borel "Topology of Lie groups and characteristic classes." Bull. Amer. Math. Soc. 61 (1955), 397–432. $\endgroup$
    – ThiKu
    Commented Apr 4, 2013 at 6:53
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    $\begingroup$ See also the references given at mathoverflow.net/questions/122083/… $\endgroup$
    – Mark Grant
    Commented Apr 4, 2013 at 12:28

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