[GAP Forum] Standardized Coset Tables from Permutation Representations

[James Read]

Dear GAP Forum,

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).

By the way, the standardization algorithm can be found on page 167 of Holt et al. - Handbook of Computational Group Theory.

Many thanks,

James Read