I've encountered a model which can be thought of as a version of the Hidden Subgroup Problem (https://en.wikipedia.org/wiki/Hidden_subgroup_problem), but that doesn't quite meet the standard problem's requirements.
Specifically, the universe group is $S_n$ (the permutation group of order $n$), and is hence not Abelian. Also, my hiding function cannot be described with a low enough number of bits.
I'm trying to show that my problem is NP-hard (which I suspect might be the case). So,
Are there any known NP-hard variants of the non-Abelian hidden subgroup problem?