A base 12 number system would have two extra symbols. Twelve would be written 10 and be called ten, and the number 144 would be written 100 and be called one hundred.

Everything you may think is inherent to base 10 is largely not. The quirky rules of 9's multiplication table would apply to 11's. Pi and e would still be irrational, and continue being no no matter which base of N you choose. Long division would work the same. Etc.