[GAP Forum] Standardized Coset Tables from Permutation Representations

[Alexander Hulpke]

Dear Forum, Dear James Read,

> Suppose I have the permutation representation of a group G on the right cosets of a subgroup H. For example, the permutation representation of the modular group on the right cosets of the principal congruence subgroup Gamma(4) is:
> 
> (1,10)(11,14)(15,23)(3,24)(2,4)(12,8)(13,16)(20,22)(6,21)(17,19)(9,18)(5,7)
> (1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)
> 
> How can I use this to produce the corresponding standardized coset table in GAP? Obviously writing down a coset table is easy by hand, but I would like to use GAP to automate the procedure and produce the corresponding standardized table (which is not so easy to just write down).

Suppose perms is a list of these permutations. Then
tab:=CosetTableBySubgroup(g,Stabilizer(g,1));
StandardizeTable(tab);

produces a standardized coset table. (Of course CosetTableBySubgroup) will also work for many other cases of subgroups).

Best,

   Alexander Hulpke