Identifying the group in GAP

Question

I am defining a matrix group in GAP. I know that its a finite group, and can compute its order. Using sonata package and commands like AllGroups( Size( G ) ) and IsIsomorphicGroup( G, H ) commands, I can find the Group-ID in the GAP database.

I would like to identify this group with a well-known group like Dihedral, Quaternion, Cyclic, etc. Is there any way to achieve this?

m1 := [[0,-1],[1,0]] ;
m2 := [[0,1],[1,0]] ;
G := Group( m1, m2 );
Size( G );

One option I can think is to define these standard groups and check if $G$ is isomorphic to any of them! For example,

IsCyclic( G ); # This is easy!
Q := QuaternionGroup( Size( G ) );
IsIsomorphicGroup( G, Q );
D := DihedralGroup( Size( G ) );
IsIsomorphicGroup( G, D );

I know the term well-known is a vague, but these are the groups, I would understand from my textbook!

A possible (vague) general question can be asked, are there named groups in GAP?

Answer 1

You might notice that $m_2$ and $m_1m_2$ both have order two, and your group is certainly generated by $m_2$ and $m_1m_2$, therefore, it must be dihedral. (In this case, of order $8$, since $m_1$ has order $4$.)