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) ] ] ] 

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