50.6 PrimeBlocks

PrimeBlocks( tbl, prime )
PrimeBlocks( tbl, chars, prime )

For a character table tbl and a prime prime, PrimeBlocks( tbl, chars, prime ) returns a record with fields

block:

a list of positive integers which has the same length as the list chars of characters, the entry n at position i in that list means that chars[i] belongs to the n-th prime-block

defect:

a list of nonnegative integers, the value at position i is the defect of the i--th block.

PrimeBlocks( tbl, prime ) does the same for chars = tbl.irreducibles, and additionally the result is stored in the irredinfo field of tbl.

    gap> t:= CharTable( "A5" );;
    gap> PrimeBlocks( t, 2 ); PrimeBlocks( t, 3 ); PrimeBlocks( t, 5 );
    rec(
      block := [ 1, 1, 1, 2, 1 ],
      defect := [ 2, 0 ] )
    rec(
      block := [ 1, 2, 3, 1, 1 ],
      defect := [ 1, 0, 0 ] )
    rec(
      block := [ 1, 1, 1, 1, 2 ],
      defect := [ 1, 0 ] )
    gap> InverseMap( last.block ); # distribution of characters to blocks
    [ [ 1, 2, 3, 4 ], 5 ]

If InfoCharTable2 = Print, the defects of the blocks and the heights of the contained characters are printed.

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