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
GAP 3.4.4