Finding and Identifying Finite Subgroups in SageMath

I have a finite subgroup, which I determined to be finite using the is_finite() function. The cardinality() function helped me establish how many matrices are present in this subgroup. Now, I am curious to know if there is a way to identify this specific finite subgroup in SageMath, for example, does it belong to the XX* subgroup? Alternatively, to which group does this subgroup belong? Perhaps there exists a database where we can conveniently check the nature of this subgroup.

I am also wondering if we can directly check if the MatrixGroup(new_matrices_) group is actually an XX* group using a function like if new_matrices == XX*. Additionally, I have a related question: How can I locate a specific subgroup in SageMath? For example, I have several subgroups defined in this paper (https://arxiv.org/pdf/hep-th/9905212.pdf), and if I want to access, let's say the XX* group, how can I do it in SageMath? Any answers related to GAP would also be very welcome, but I'm not sure how to convert a matrix group in SageMath to GAP. Sorry for the many little questions. I thought that they are all related, so instead of asking a new question for each little question, I combined them into one question and asked them all together.

• I think this question is probably a better fit at ask.sagemath.org. There are people here who know quite a bit about sage, but at ask.sagemath.org everybody knows quite a bit about sage, so you're likely to get an answer more quickly ^_^ Commented Jul 18, 2023 at 16:09
• sagemath is really worse in that sense. I also thought what you said. Once I asked a question there (2 weeks ago), still no answer. However, I got the answer here in 2 days Commented Jul 18, 2023 at 23:52
• Please give the code for that one finite subgroup. For me, the XX* does not ring any bell. What do you want at that point? It is also unclear what "locate" and "access" mean. First of all, please introduce the group (providing code), if you can introduce it, else if there should be some "access based on structure", please give us the structure. Depending on it the group is constructed humanly using the few / many ways to do so. The linked paper has some tables with groups labeled by roman numerals, but it takes a long time to understand the notations. Just fix one such group here... Commented Jul 21, 2023 at 17:19