Marks Tables

multiplication table 4×4
K4 = alt( 2(2) )

C3 = alt( 3 )

2(1∙1) = alt( C4 )

2(1∙1) = alt( 2.2 )

1∙1∙1∙1 = alt( 1∙1∙2 )

The table of marks for the symmetric group S3:

the marks of S4
(from Naugton 2013)

The permutations of a normal subgroup H fixes all cosets σH; The normals subgroups of S4 are visible above: S4,A4, Klein and Id.