# How do Galois fields of sizes other than powers of primes behave? [duplicate]

I understand how Galois fields of prime powers (e.g. $GF(2^8)$, $GF(17)$, $GF(257)$) behave. What I could never figure out is how they behave with sizes other than simple powers of primes. For example, $GF(15)$, $GF(100)$, or $GF(2^43^5)$.

Is it even possible?