I’ve now understood more of turings design, in his on permutations paper.
It’s common to use Q as the letter for positive definite forms. And one then uses it to average over the group.
There are many Q, since the domain can be over 1 letter back in the cipher text, or 2, or 3… as his Lemma was pointing out (v obliquely). They are all the same, since it’s the invariance one is relying on.
Also see now the basis for his argument why some generators are 1 while the rest is 0.