A tensegrity is a structure made from cables, struts and stiff bars. A d-dimensional tensegirty is universally rigid if it is rigid in any dimension d′ with d′≥d. The celebrated super stability condition due to Connelly gives a sufficient condition for a tensegrity to be universally rigid. Gortler and Thurston showed that super stability characterizes universal rigidity when the point configuration is generic and every member is a stiff bar. We extend this result to tensegrities with point group symmetry, and show that the characterization still holds as long as a tensegrity is generic modulo symmetry. Our strategy is based on the block-diagonalization technique for symmetric semidefinite programming problems. This is joint work with Shin-ichi Tanigawa.