# 86.4 PointsAndRepresentativesOrbits

`PointsAndRepresentativesOrbits( G[, m] )`

returns a pair [orb, rep] where orb is a list of the orbits of the permutation group G on `[ 1..LargestMovedPoint( G ) ]` and rep is a list of list of elements of G such that `rep[i][j]` applied to `orb[i][1]` yields `orb[i][j]` for all i,j. If the optional argument m is given, then `LargestMovedPoint( G )` is replaced by the integer m.

```    gap> G := Group( (1,7)(2,3)(5,6)(8,9)(11,12),
>                (1,5)(2,8)(3,4)(7,11)(9,10) );;
gap> PointsAndRepresentativesOrbits( G );
[ [ [ 1, 7, 5, 11, 6, 12 ], [ 2, 3, 8, 4, 9, 10 ] ],
[ [ (), ( 1, 7)( 2, 3)( 5, 6)( 8, 9)(11,12),
( 1, 5)( 2, 8)( 3, 4)( 7,11)( 9,10),
( 1,11,12, 7, 5, 6)( 2, 4, 3, 8,10, 9),
( 1, 6, 5, 7,12,11)( 2, 9,10, 8, 3, 4),
( 1,12)( 2, 4)( 3, 9)( 6, 7)( 8,10) ],
[ (), ( 1, 7)( 2, 3)( 5, 6)( 8, 9)(11,12),
( 1, 5)( 2, 8)( 3, 4)( 7,11)( 9,10),
( 1,11,12, 7, 5, 6)( 2, 4, 3, 8,10, 9),
( 1, 6, 5, 7,12,11)( 2, 9,10, 8, 3, 4),
( 1, 6)( 2,10)( 4, 8)( 5,11)( 7,12) ] ] ] ```

GAP 3.4.4
April 1997