Can I use GAP to show block structures in a multiplication group clearer $\ $?

Question

The usual output of GAP for the multiplication table of the group $S3$ is

$$\pmatrix{1&2&3&4&5&6\\2&1&4&3&6&5\\3&6&5&2&1&4\\4&5&6&1&2&3\\5&4&1&6&3&2\\6&3&2&5&4&1}$$

The table

$$\pmatrix{1&2&3&4&5&6\\2&3&1&6&4&5\\3&1&2&5&6&4\\4&5&6&1&2&3\\5&6&4&3&1&2\\6&4&5&2&3&1}$$

would show the block-structure (two $3\times 3$ blocks with entries $1-3$ and two $3\times 3$-blocks with entries $4-6$) much clearer.

Can I display such a multiplication table with gap ?

Answer 1

Let N be a normal subgroup of G. Then

MultiplicationTable(Flat(List(RightCosets(G, N),i->List(i))));

produces a table with block structure.

For example:

gap> G:=QuaternionGroup(8);                                                    
<pc group of size 8 with 3 generators>
gap> N:=NormalSubgroups(G)[5];                                              
Group([ y2 ])
gap> Display(MultiplicationTable(Flat(List(RightCosets(G, N),i->List(i)))));
[ [  1,  2,  3,  4,  5,  6,  7,  8 ],
  [  2,  1,  4,  3,  6,  5,  8,  7 ],
  [  3,  4,  2,  1,  8,  7,  5,  6 ],
  [  4,  3,  1,  2,  7,  8,  6,  5 ],
  [  5,  6,  7,  8,  2,  1,  4,  3 ],
  [  6,  5,  8,  7,  1,  2,  3,  4 ],
  [  7,  8,  6,  5,  3,  4,  2,  1 ],
  [  8,  7,  5,  6,  4,  3,  1,  2 ] ]