### 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, is it actually 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 MatrixGroup(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: A Monograph on the Classification of the Discrete Subgroups of SU (4), and if I want to access, let's say the XX* subgroup, how can I do it in SageMath? 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.