48.20 CharTableIsoclinic

CharTableIsoclinic( tbl )
CharTableIsoclinic( tbl, classes_of_normal_subgroup )

If tbl is a character table of a group with structure 2.G.2 with a unique central subgroup of order 2 and a unique subgroup of index 2, CharTableIsoclinic( tbl ) returns the table of the isoclinic group (see~cite[Chapter 6, Section 7]CCN85); if the subgroup of index 2 is not unique, it must be specified by enumeration of its classes in classes_of_normal_subgroup.

    gap> d8:= CharTable( "Dihedral", 8 );;
    gap> PrintCharTable( CharTableIsoclinic( d8, [ 1, 2, 3 ] ) );
    rec( identifier := "Isoclinic(D8)", size := 8, centralizers :=
    [ 8, 4, 8, 4, 4 ], classes := [ 1, 2, 1, 2, 2 ], orders :=
    [ 1, 4, 2, 4, 4 ], fusions := [  ], fusionsource := [  ], powermap :=
    [ , [ 1, 3, 1, 3, 3 ] ], irreducibles :=
    [ [ 1, 1, 1, 1, 1 ], [ 1, 1, 1, -1, -1 ], [ 1, -1, 1, 1, -1 ],
      [ 1, -1, 1, -1, 1 ], [ 2, 0, -2, 0, 0 ]
     ], operations := CharTableOps, order := 8, name := "Isoclinic(D8)" )

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