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The Rubik's Cube Group has order $2^{27} 3^{14} 5^3 7^2 11$. What is known about the Sylow subgroups of this group? Do they have an intuitive meaning with regards to the symmetry of the cube?

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    $\begingroup$ This problem is amenable to the free software GAP: see here (39.13-1) and here. $\endgroup$ – Shaun Apr 3 '19 at 18:28
  • $\begingroup$ Here is the gap tag. If you're happy with computing the subgroups, then I suggest you add it with an edit. $\endgroup$ – Shaun Apr 3 '19 at 18:59
  • $\begingroup$ There are even questions having both gap and rubiks-cube tags, e.g. this $\endgroup$ – Alexander Konovalov Apr 3 '19 at 20:44

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