A*BCDEF=GGGGGG -> A*BCDEF=(111111)*G. Now, 111111 = 3*7*11*13*37, and accordingly, A = 3 or 7.

If A =3, then BCDEF = (37037)*G, so that:
G = 1,2,  giving: BCDEF = 37037, 74074. This is a contradiction, since we do not obtain all distinct values for B, C, D, E and F.

Accordingly, A= 7, so that: BCDEF = (15873)*G, and accordingly: G <= 6

Now, we observe that:

G = 1 -> BCDEF = 15783
 
G = 2 -> BCDEF = 31566

G = 3 -> BCDEF = 47349

G = 4 -> BCDEF = 63132

G = 5 -> BCDEF = 78915

G = 6 -> BCDEF = 95238

From the above table, we observe that there are duplicate letters that are assigned to at least one digit, unless G =6

Consequently, the required value of G is 6.