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Describing the Sylow 2-subgroups of S5

  1. Jul 24, 2009 #1
    What is a good way to describe and count the Sylow 2-subgroups of S5? The ones isomorphic to D8 should be simple enough to describe as the extra conjugates of the Sylow 2-subgroups of S4, but I am trying to figure out how to easily describe any/all those isomorphic to Q8, which don't exist in S4.
  2. jcsd
  3. Jul 25, 2009 #2
    All Sylow p-subgroups of any group G are isomorphic (conjugate, in fact). Thus, if you can identify one copy of D8 in S5, you can immediately conclude that all Sylow 2-subgroups of S5 are isomorphic to D8.
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