I know that there exist classification theorems for real, complex, and quaternionic, reflection groups.

There are presentations for the real reflection groups, as well as further presentations for the complex ones. The ones for the quaternions and the complex numbers are less familiar, and, from what I can see, their Dynkin diagrams and Weyl symbols are not standardised like the real ones. There are also the three infinite families (discussed by Broué, Malle, and Rouquier in their paper on complex reflection groups).

I did try to see if anyone had attempted to classify the octonionic reflection groups. But as far as I could tell, no one has attempted to derive the complete set. If this has already been done, then please refer me to an open access source. If not then this’ll probably be an open problem, but I am nowhere near experienced enough in the topic of reflection groups to even attempt a classification.

Here is the paper on complex reflection groups: https://www.math.ucla.edu/~rouquier/papers/banff.pdf

hyperbolicreflection groups” which are not what I am asking about. I am asking aboutfinitegroups. $\endgroup$groupswhich would by definition, imply associativity. here is the reference tohyperbolicoctonionic reflection groups: ma.utexas.edu/users/allcock/research/oh2.pdf $\endgroup$1more comment