GAP Manual: 7.5. Order

Order( G, g )

Order returns the order of a group element g in the group G.

The order is the smallest positive integer i such that g^i is the identity. The order of the identity is one.

    gap> Order( Group( (1,2), (1,2,3,4) ), (1,2,3) );
    3
    gap> Order( Group( (1,2), (1,2,3,4) ), () );
    1