Thank you for reporting this.  I have created an SCR for the error resulting from attempting to call the Subgroup method on the left coset.   This is supposed to work correctly in the same way that, for example, the Elements method ultimately gets called despite there being a package export of the same name.

@Carl Love  I've created a (separate) bug report for this instance in which valid digraphs are input.  Thanks for finding this example!

@Markiyan Hirnyk Thank you for your interest in the GroupTheory package.  I have posted a reply to the original question.

Suggestions for things to improve are always welcome, and the isomorphism algorithm is much improved in Maple 17.  I checked Pablo Spiga's census of cubic vertex-transitive graphs from http://www.matapp.unimib.it/~spiga/census.html.  For each of the 105 graphs there of order 120, a randomly generated isomorphic copy was produced and tested for isomorphism with the original graph.  Taking the average over 5 (randomized) trials per graph, the average time in Maple 17 to detect isomorphism was about 0.094sec.  I did the tests on an Intel Core2 Quad 2.40 GHz machine with Ubuntu Linux.

James McCarron, Mathematics, Maplesoft

Thanks very much for the valuable feedback.  We'll certainly consider your suggestions for future Maple releases.

James McCarron, Maplesoft

@Alec Mihailovs 

These are great suggestions, and I'm glad to hear there is interest in work in these areas.

Sure. The 'monoid' property is one of the builtin properties, so you can just pass that name as a keyword option. The command

> Magma:-Enumerate( 6, 'monoid' );
                             2237

does the job. Using this, it is easy to construct a table of the numbers of isomorphism classes of monoids up to order 7.

  Order        No. Monoids
    2                 2
    3                 7
    4                35
    5               228
    6              2237
    7             31559
    8           1668997

The order 8 result takes quite awhile to run, and saving the results produced a file of about 350 Mb!

@Alec Mihailovs 

 Thank you.  Your kind feedback is appreciated.