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?