579085261 is CRAZY, 725582 is GOLF, 10757494 is ...?
Jelly, 29 27 bytes

ÆEµØA“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?xḊṚḢ}¡


Thanks to @JonathanAllan for golfing off 1 byte!

Try it online!

Background

“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’


is a numeric literal. The characters between the quotes are replaced with their 1-based indices in the Jelly code page, and the resulting array is interpreted as a base-250 number. This yields the integer c := 288824892868083015619552399.

How it works

ÆEµØA“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?xḊṚḢ}¡  Main link. Argument: n

ÆE                           Yield the exponents of n's prime factorization, with.
                             zeroes. This yields an array A.
  µ                          Begin a new monadic chain with argument A.
   ØA                        Set the return value to “ABC...XYZ”.
     “¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?        Select the c-th permutation of the alphabet, yielding
                             s := “SPMFLQUIXNCWORAGZTEJHVDBKY”.
                      Ḋ      Dequeue; yield A without its first element, stripping
                             the exponent of 2.
                     x       Repeat the k-th letter of s r times, where r is the
                             exponent of the k-th odd prime number.
                          ¡  Combine the two links to the left into a quicklink:
                        Ḣ}     - Apply head to the right argument (A), yielding the
                                 exponent of 2. Since n is at most divisible by the
                                 first power of 2, this yields 1 for even numbers
                                 and 0 for odd ones. Call the link to the left that
                                 many times on the previous return value.
                       Ṛ       - Reverse the string to the left.