- #1
R.P.F.
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Homework Statement
Find the smallest integer n such that the quaternion group G has a faithful operation on a set Sof order n.
Homework Equations
The Attempt at a Solution
So the homomorphism between G and permutations of S is injective. which means the order of S_n is bigger than or equal to the order of G. so we should start from n=4. Is it possible to find a subgroup of S_4 that's isomorphic to G. I think the answer is no. so we go to n=5,6 and so on. I'm having trouble finding such a subgroup.
Thanks!