Monstrous moonshine associates to every element of order
where
In snakes, spines, and all that we’ve constructed the arithmetic group
which normalizes
I’m sure one can describe this subgroup explicitly in each case by analysing the action of the finite group
But at the moment I don’t understand the general construction given by Conway, McKay and Sebbar in On the discrete groups of moonshine. I’m stuck at the last sentence of (2) in section 3. Nothing a copy of Charles Ferenbaugh Ph. D. thesis cannot fix.
The correspondence between the conjugacy classes of the Monster and these arithmetic groups takes up 3 pages in Conway & Norton’s Monstrous Moonshine. Here’s the beginning of it.