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.