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Somewhat surprisingly I was unable to find any tables for the number of positions of various lengths in ascending order for this order 170659735142400 group w.r.t. three mutually orthogonal face generators such as U,F and R, i.e. This is seemingly beyond the reach of conventional software tools to solve, so I am appealing to the seemingly large number of contributors who have developed their own bespoke utilities. I'd be grateful if a table could be posted here. In particular is the diameter of the Cayley graph for this known?