G/C ?
Are you sure it was not C/G?
C/G is standard chord notation for playing the C chord with G in the bass, in other words, the second inversion. (i.e G - C - E, instead of C- E-G)
G/C would mean the G chord (GBD) with C in the bass - but as you can see, C is not part of the G chord - does not mean that you cannot do it, just unusual.
Best wishes,
Bernhard.