GAP Manual: 7.51. Index

Index( G, U )

Let U be a subgroup of G. Then Index returns the index of U in G as an integer.

Note that Index sets and checks U.index if G is the parent group of U.

    gap> s4 := Group( (1,2,3,4), (1,2) );
    Group( (1,2,3,4), (1,2) )
    gap> Index( s4, DerivedSubgroup( s4 ) );
    2 

The default function GroupOps.Index needs a finite group G. It returns the quotient of Size( G ) and Size( U ).