Suffix array construction algorithm linear complexity constant
Constants like this are generally not calculated for the run time of algorithms, because it's not clear what they would count - would they count the number of some sort of primitive C operation executed, or the number of x86-64 operations, or the number of arm64 operations, or the microcode operations, or ...?

More frequently than calculating the constants, people measure the run time and show the $\alpha$ that fits best. They will also sometimes calculate the number of times a specific operation is executed, like comparisons or swaps in a sorting algorithm.