Some properties fail for reasonably small values of n but those values don't seem small when there is a lot of work involved even in the small cases, or in which there is a certain resistance to the idea for some reason. Thus counterexamples may be found even after what is seen, after the fact, as a small number of previous cases. Here are some examples. George Berzsenyi first asked about this sort of question in the January 1996 issue of Quantum magazine. Stan Wagon posed the first problem as one of his Problems of the Week and Ilan Vardi provided the subsequent examples.
Deep ideas are simple.
Odd groups are even. Mathieu group, M24. My favourite small number example is take a circle. Here are some examples. George Berzsenyi first asked about this sort of question in the January 1996 issue of Quantum magazine.