RepresentativesPowermaps( listofpowermaps, matautomorphisms )
returns a list of representatives of the list listofpowermaps of powermaps under the operation of a subgroup matautomorphisms of the maximal admissible subgroup of matrix automorphisms of irreducible characters 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> Powermap( t, 3 ); [ [ 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 ], [ 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 ] ] gap> RepresentativesPowermaps( last, 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 ] ]
GAP 3.4.4