GAP Manual: 6.2. Field

Field( z,.. ) Field( list )

In the first form Field returns the smallest field that contains all the elements z,.. etc. In the second form Field returns the smallest field that contains all the elements in the list list. If any element is not an element of a field or the elements lie in no common field an error is raised.

    gap> Field( Z(4) );
    GF(2^2)
    gap> Field( E(9) );
    CF(9)
    gap> Field( [ Z(4), Z(9) ] );
    Error, CharFFE: <z> must be a finite field element, vector, or matrix
    gap> Field( [ E(4), E(9) ] );
    CF(36) 

Field differs from DefaultField (see DefaultField) in that it returns the smallest field in which the elements lie, while DefaultField may return a larger field if that makes sense.