What is the group of pointed homotopy classes of maps from $S^3 \times S^3$ to $S^3$?  The group structure induced by the group structure on the codomain.  This question is a followup to Eric's answer to [another question][1].


  [1]: http://mathoverflow.net/questions/160285/can-the-group-of-homotopy-classes-of-maps-into-s3-be-noncommutative