Generalized 6j symbols for G2 in which all four triangular conditions involve the seven-dimensional irreducible representation (irrep) (10) are multiplicity-free. Algebraic expressions depending on the highest weights of the accompanying irreps are found by using generalizations of the Racah-Wigner algebra. A rule is given for generalizing the SO(3) phase factors. The results are applied to finding algebraic expressions for a class of isoscalar factors for SO(7)⊇G2.