I'd like to transpose a sample (in cents) from G Minor to C Major.
How do I do that, or is it even possible?
You can't just transpose a minor key into a major key, because a minor scale has a different structure than a major scale.
Natural minor scale in steps: whole, half, whole, whole, half, whole, whole
Major scale in steps: whole, whole, half, whole, whole, whole, half
Because you've talked about cents... 100 cents are equal to one semitone.
So you could transpose a G major scale into a C major scale, by transposing each note in the key of G major either 5 semitones (500 cents) up, or 7 semitones (700 cents) down.
But again, this doesn't work for major into minor keys or vice versa, because if you would transpose the minor chords of G minor up or down, they still maintain minor chords, so they would have chromatic chord notes, that are actually not in the scale of C major.
And with samples, you basically have no chance at all to transpose anything from minor to major or vice versa. You can transpose them up or down in pitch, but they would always maintain major or minor.
You could transpose the G minor sample to A minor, which is the relative minor of C Major, which means that it uses the same notes as C Major and the sample won't clash (too much) with other elements in C Major. You'll have to judge whether the combination of A minor and C Major elements in the track sounds good or not on a case by case basis.
That would mean tuning it up by two semitones, or +200 cents. If you transpose without resampling, this will also speed the sample up by 12.25%.
Depending on the specific notes being played in the sample and in the rest of the track, other transpositions might work too, especially to D minor (+700 or -500 cents) and E minor (-300 cents).
A simple transposition won't be able to change a sample from minor to major, because a transposition won't change the frequency ratios between the notes (which is what's required to be able to change the tonality).
One answer might be to use a special kind of audio editor that can pick out the individual notes in an audio recording. Celemony's Melodyne is the best-known example of this kind of program.