Abstract
A real representation π of a finite group may be regarded as a homomorphism to an orthogonal group O(V). For symmetric groups Sn, alternating groups An, and products Sn×Sn′ of symmetric groups, we give criteria for whether π lifts to the double cover Pin(V) of O(V), in terms of character values. From these criteria we compute the second Stiefel-Whitney classes of these representations.
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