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The notes of the G-sharp major scale are: G#, A#, B#, C#, D#, E#, Fx, G#. The x you see is called a double sharp. (Double sharps raise a note higher by 1 whole step. Fx is actually G.) However, because of the simpler enharmonic equivalent of Ab major, which has 4 flats, Ab major is used a lot more than G# major ever is.
E will be the 3rd note of the chord and G will be the 5th note of the chord. When comparing these notes to the scale/key of the chord (C), which in the case of the root chord will be the same scale/key we are harmonizing, we have a 1, 3, 5 which is the formula for any Major chord. So chord I of the harmonized C Major scale is C Major.