Assume that G of order 48 has 3 sylow 2-subgroups. Let G act on the set of such subgroups by conjugation. How do I know that this action is onto? I know that all 3 subgroups are conjugate but I'm not sure this is enough.
I can't imagine this is too difficultto find that an action is onto i.e. can I map to every permutation in S3. My problem is (1 2 3) is in S3 so is this telling me I need to find a g such that gHg^-1=M, gMg^-1=K and gkg^-1=H, for the slylow subgroups H,k,M