Quaternion Group as Permutation Group I was recently, for the sake of it, trying to represent Q8, the group of quaternions, as a permutation group. I couldn't figure out how to do it.
So I googled to see if somebody else had put the permutation group on the web, and I came across this:
http://mathworld.wolfram.com/PermutationGroup.html

Not all groups are representable as permutation groups. For example, the quaternion group cannot be represented in terms of permutations. 

This strikes me as a very odd statement, because I quickly checked this:
http://mathworld.wolfram.com/CayleysGroupTheorem.html

Every finite group of order n can be represented as a permutation group on n letters

So it seems Q8 should be representable a sa permutation group on 8 letters.
How can these two quotes be reconciled?


Not all groups are representable as permutation groups. For example,
  the quaternion group cannot be represented in terms of permutations.

For the record, the page you linked to doesn't say this anymore. I'm guessing they recognized it was an error and removed it some time in the last three years.
