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?
StructureDescription
: Note thatStructureDescription
is not intended to be a research tool, but rather an educational tool. $\endgroup$IdGroup
. $\endgroup$