How do you use GAP to identify the name of a group from its multiplication table? I know that you can define a group from a set of generators, and then look for the group in the set of internal tables:
gap> g := Group([ (1,2), (1,2,3,4,5) ]);
Group([ (1,2), (1,2,3,4,5) ])
gap> IdGroup(g);
[ 120, 34 ]
But how do find out the name of the group [120, 34]
?
The StructureDescription command might do what you need. For example,
gap> StructureDescription(g);
returns "S5" for your example, the symmetric group on five elements. For comparison,
gap> StructureDescription(SmallGroup(120,35));
gives "C2 x A5" and
gap> StructureDescription(SmallGroup(120,36));
gives "S3 x (C5 : C4)". I don't know at what point these descriptions fall below the level of naming the group, but is this on the track you want?