I have been playing around with representations of discrete groups using the GAP software and I have noticed that PSL(2,7) is the only group (as far as I can find) with a tensor product expansion 3x3=6+3'. 6 is symmetric and 3' is antisymmetric. ie. PSL(2,7) is the only group having the tensor product of two 3s decomposing into two representations- one of which consisting of all the symmetric combinations and the other one consisting of all the antisymmetric combinations. Is this observation correct?