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  • $\begingroup$ Would you be willing to add another example or two? The scope of your question is not clear to me. Does your input always reduce to a simple CyclicGroup or do you need something more robust than that? $\endgroup$ Commented Nov 12, 2014 at 13:04
  • $\begingroup$ @Mr.Wizard: Cannot add another example right now, but in general I have a (possibly large) mult table for a group, and I would like to get a Mathematica group object out of it. Could be any finite group. $\endgroup$ Commented Nov 12, 2014 at 13:53