Are you counting groups as distinct that are identical to each other, but happen to use different numbers for the elements? For example, {1, 3, 7, 9} is really the same group as {6, 2, 8, 4} (the elements correspond in the order listed). Does it makes sense to count it twice? If so, then we're really identifying subsets of integers that generate these groups, rather than the groups themselves. Tom Keith F. Lynch writes:
This is a simple finite group problem, not to be confused with a finite simple group problem. It's a simple problem about finite groups, not a difficult problem about finite simple groups.
List all multiplicative groups of integers mod ten. For instance {1,9} is one of them, and {1} is another.
I noticed that the number of multiplicative groups of integers mod N is not in OEIS. I plan to add it.
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