# What is the second stiefel whitney class of SO(n)?

$\omega_2(SO(n))=?$, that is, What is the second stiefel whitney class of SO(n)?

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What vector bundle did you have in mind? –  Grumpy Parsnip Apr 21 '11 at 16:52

$SO(n)$ is a Lie group and so its tangent bundle is trivial. Thus $w_2(TSO(n)) = 0$.