The positions a 3x3x3 may be placed in by rotating the faces may be represented as a mathematical group. The size of this group is 43,252,003,274,489,856,000 and may be calculated in the manner shown in the video. This is the "real" size of the group.

When one is performing "god's algorithm" calculations one may reduce the number of calculations using cubic symmetry and inversion arguments as the video and Herbert Kociemba have pointed out above. If one grinds out an optimal solution for a position, one may easily and quickly generate optimal solutions for potentially 96 different positions using symmetry and inversion. Nevertheless, these are different positions and one hasn't really "reduced the size of the group".