1. The problem asks us to find the number that should replace the gap in the equation $$(26 \times 37) \times 12 = \square$$ given that $$26 \times (37 \times 12) = 11544$$. 2. By the associative property of multiplication, the grouping of factors does not change the product. So, $$26 \times (37 \times 12) = (26 \times 37) \times 12$$. 3. Since $$26 \times (37 \times 12) = 11544$$, it follows that $$(26 \times 37) \times 12 = 11544$$. 4. Therefore, the number that should go in the gap is $$11544$$. Final answer: $$\boxed{11544}$$.