I have got a permutation group:
$(\{(e,((1, 4),(2,6),(3,5)),((1, 6),(2,5),(3,4)),((1, 5),(2,4),(3,6)),((1, 3,2),(4,6,5)),((1,2,3),(4,5,6)),((1, 4),(2,5),(3,6)),((1, 3),(4,6)),((2, 3),(5,6)),((1, 2),(4,5)),(1,6,2,4,3,5),(1,5,3,4,2,6)\},\circ)$
I want to create a group table for this and can't seem to find how to achieve it.
In my mind I can see that I need to pass each permutation to Mathematica and then get it to simply generate the group table however achieving this does not seem that simple!
I also would like the group table to match the ordering of the permutations above rather than Mathematica's default ordering, the permutations to be labelled e,a,b,c,d,f,r,s,t,u,v,w respectively and the order of composition of permutations to be column * row not Mathematica's default row * column.
{Cycles[{}], Cycles[{{1, 4}, {2, 6}, {3, 5}}], Cycles[{{1, 6}, {2, 5}, {3, 4}}], ...}
. $\endgroup$