Flying by plane is incredible cheap compared to railway not only on that connection unfortunately.

The plane business is extremely cost effective organized (not only thanks to cheap players like RyanAir) and benefits a lot from state sponsored infrastructure (airports, ATC) and subsidized resources (no Kerosene tax) compared to railways which need more infrastructure (tracks everywhere instead of "simply" using air) and need to refinance having trains going "everywhere"

The railway ticket to and from the airport is almost more expensive than a flight across the continent ...