a) Show that if $\phi$ from $S_5$ to $S_6$ is any exotic map, then $\phi$ is injective, and moreover $phi$ doesn't send transpositions to transpositions.
b) If $\phi$ is as in part a), show that $\phi(A_5)$ is contained in $A_6$ and conclude that $H$=$Im(\phi)$ contains no transpositions.
Admittedly I couldn't make much progress in this problem, primarily because I don't really understand the exotic map to start with. I scoured around the internet but information on exotic map is really scarce and not very useful.
I also looked at the example of the mystic pentagons, but it wasn't of much help really.
Any help much appreciated. Especially if someone can explain exotic map to me that'd be so great.