We classify G-invariant subvarieties of the 3-tensor space C^2⨂C^2⨂C^2 that are defined by polynomials with degree≤6,where G=GL(2,C)×GL(2,C)×GL(2,C). We also calculate the character fo S^p(C^2⨂C^2⨂C^2), determine the generators of each irreducible component of S^p(C^2⨂C^2⨂C^2), and obtain some curious identities between them that play a fundamental role in classifying invariant subvarieties
