[GAP Forum] Naming of Primitive Groups

[Chris Jefferson]

After trying to track down some strange behavior in a program, I was 
surprised to find the names of the first two primitive groups of size 10:

gap> PrimitiveGroup(10, 1);
A(5)
gap> PrimitiveGroup(10, 2);
S(5)

These are, unsurprisingly, the same names as:

gap> PrimitiveGroup(5,4);
A(5)
gap> PrimitiveGroup(5,5);
S(5)

Out of curiosity, are these groups related in some non-obvious way, and 
is there any reason the names of the primitive groups are not unique?

Chris