51.26 OrbitPowermaps

OrbitPowermaps( powermap, matautomorphisms )

returns the orbit of the powermap powermap under the operation of the subgroup matautomorphisms of the maximal admissible subgroup of the matrix automorphisms of the corresponding character table.

    gap> t:= CharTable( "3.McL" );;
    gap> maut:= MatAutomorphisms( t.irreducibles, [], Group( () ) );
    Group( (55,58)(56,59)(57,60)(61,64)(62,65)(63,66), (35,36), (26,29)
    (27,30)(28,31)(49,52)(50,53)(51,54), (40,43)(41,44)(42,45), ( 2, 3)
    ( 5, 6)( 8, 9)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)
    (38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)
    (65,66) )
    gap> OrbitPowermaps( t.powermap[3], maut );
    [ [ 1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 11, 11, 11, 14, 14, 14, 17, 17, 17,
          4, 4, 4, 4, 4, 4, 29, 29, 29, 26, 26, 26, 32, 32, 32, 8, 9, 37,
          37, 37, 40, 40, 40, 43, 43, 43, 11, 11, 11, 52, 52, 52, 49, 49,
          49, 14, 14, 14, 14, 14, 14, 37, 37, 37, 37, 37, 37 ], 
      [ 1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 11, 11, 11, 14, 14, 14, 17, 17, 17,
          4, 4, 4, 4, 4, 4, 29, 29, 29, 26, 26, 26, 32, 32, 32, 9, 8, 37,
          37, 37, 40, 40, 40, 43, 43, 43, 11, 11, 11, 52, 52, 52, 49, 49,
          49, 14, 14, 14, 14, 14, 14, 37, 37, 37, 37, 37, 37 ] ]

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