What's the reason for the huge increase in price between car and aviation gas?
There are many differences, as other answers mentioned, but not as big as the experienced prices show. But by only focusing on the product it's easy to miss cost involved in distribution and sales.
An FBO has at least the same, usually much higher, fixed cost than an average gas station which need to be spread over a much lower number of customers. The fact that a C172 needs more gas (like 50 vs. 15 gallons) isn't much of a relief either.
In addition I don't know of many gas stations providing a lounge, free coffee (and sometimes sandwiches), internet access, flight planing tools and so on, all the way to courtesy cars.
All of this leads to a higher price per gallon than what's caused by the raw gas alone. The effect can be easily seen where auto gas is offered for ultralights, or diesel for capable engines. They carry a visible mark up compared to the gas station next door.
Then of course there's the same effect that lack of competition has on auto gas. Fields with a single FBO are often priced much like the sole gas station on a lengthy stretch of highway ... slightly above average.