We consider both facial reduction,FR, and symmetry reduction,SR, techniques for semidefinite programming,SDP. We show that the two together fit surprisingly well in an alternating direction method of multipliers,ADMM, approach. In fact, this approach allows for simply adding on nonnegativity constraints, and solving the doubly nonnegative,DNN, relaxation of many classes of hard combinatorial problems. We also show that the singularity degree remains the same afterSR, and that theDNNrelaxations considered here have singularity degree one, that is reduced to zero afterFR. The combination ofFRandSRleads to a significant improvement in both numerical stability and running time for both theADMMand interior point approaches. We test our method on variousDNNrelaxations of hard combinatorial problems including quadratic assignment problems with sizes of more than\documentclass[12pt]{minimal}
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				\begin{document}$$n=500$$\end{document}n=500. This translates to a semidefinite constraint of order 250, 000 and\documentclass[12pt]{minimal}
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				\begin{document}$$625\times 10^8$$\end{document}625×108nonnegative constrained variables, before applying the reduction techniques.