g = h
g < h
The equality operator = evaluates to true if the group elements g
and h are equal and to false otherwise. The inequality operator
< evaluates to true if the group elements g and h are not equal
and to false otherwise.
You can compare group elements with objects of other types. Of course they are never equal. Standard group elements are permutations, ag words and matrices. For examples of generic group elements see for instance DirectProduct.
g < h
g <= h
g = h
g h
The operators <, <=, = and evaluate to true if the group
element g is strictly less than, less than or equal to, greater than or
equal to and strictly greater than the group element h. There is no
general ordering on group elements.
Standard group elements may be compared with objects of other types while generic group elements may disallow such a comparison.
GAP 3.4.4