GAP Manual: 51.30. Powmap

Powmap( powermap, n )
Powmap( powermap, n, class )

The first form returns the n-th powermap where powermap is the powermap of a character table (see Character Table Records). If the n-th position in powermap is bound, this map is returned, otherwise it is computed from the (necessarily stored) powermaps of the prime divisors of n.

The second form returns the image of class under the n-th powermap; for any valid class class, we have Powmap( powermap, n )[ class ] = Powmap( powermap, n, class ).

The entries of powermap may be parametrized maps (see More about Maps and Parametrized Maps).

    gap> t:= CharTable( "3.McL" );;
    gap> Powmap( t.powermap, 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, 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> Powmap( t.powermap, 27 );
    [ 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, 1, 1, 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> Lcm( t.orders ); Powmap( t.powermap, last );
    27720
    [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
      1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
      1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]