The determinant of G is (441*2^74)^2.
G is not unique - there is another Gram matrix (given here in compressed format) with the same determinant but different characteristic equation. On this page we restrict our attention to solutions with Gram matrix G.
By row/column switching the matrix R generates a "giant" self-dual ST-class of size 2867510353 HT-classes. In terms of Hadamard classes, the size of the giant class is 5735015027 = 2*2867510353 - 5679, since every non-self-dual HT class splits into two Hadamard classes.
The largest known class, apart from the "giant" class, is a class of size 2136 (measured in ST-classes). The full class is here and a generator is here.
Generators for the 20 largest known ST classes (excluding the giant class) are here. They generate 22888 HT-classes of (conjectured) maxdet matrices. The full set of 22888 HT-classes is here. They all have determinant +-441*2^74.
105485 HT classes not in the giant class are here (16MB, compressed using bzip2). Row/column switching (and transposition) from this list can generate a total of 3564048 HT-equivalence classes (7126516 Hadamard equivalence classes) not in the giant class. This requires 63 iterations. The complete file of 3564048 HT-equivalence classes is here (453MB, compressed using bzip2).
Note: you might find wget useful for downloading these large files.
ST10a..ST19a (one each of sizes 10..19)
ST66a (size 66)
ST100a (size 100)
ST200a (size 200)
ST999a (size 999)
ST999b (size 999, different)
ST2136a (size 2136)