GAP Manual: 8.15. OrbitLength

OrbitLength( G, d )
OrbitLength( G, d, operation )

OrbitLength returns the length of the orbit of the point d, which may be an object of arbitrary type, under the group G. See Orbit for the definition of orbits.

OrbitLength accepts a function operation of two arguments d and g as optional third argument, which specifies how the elements of G operate (see Other Operations).

    gap> g := Group( (1,2,3)(6,7), (3,4,5)(7,8) );;
    gap> OrbitLength( g, 1 );
    5
    gap> OrbitLength( g, 10 );
    1
    gap> OrbitLength( g, [1,6], OnPairs );
    15 

OrbitLength calls
G.operations.OrbitLength( G, d, operation )
and returns the value. Note that the third argument is not optional for functions called this way.

The default function called this way is GroupOps.OrbitLength, which performs an ordinary orbit algorithm. Special categories of groups overlay this default function with more efficient functions.