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Following on from a highly symmetric presentation I supplied for the miniature Rubiks cube group Presentation for the 2x2x2 Rubiks cube group I investigated whether the Mathieu Group M24 could be similarily presented taking full advantage of the plentiful symmetry inherent in the Rubiks Revenge cube (4x4x4). The answer was indeed yes - here is the presentation I found - again on three involutions:

< a,b,c | a² = b² = c² = 1,

   (ab)⁶ = [(bc)⁶] = [(ca)⁶] = 1,

   bacabacacabacababacabac = 1,

   (ababacbc)³ = 1,

   bababcbcbcbabab = cacabacacabacac >