How to do a group StructureDescription in Sage?

Question

In Sage I executed the following commands:

 F.<x, y> = FreeGroup()
 G=F / [x^2*y^-1, x^3*y^2, x*y*x^-1*y^-1]

Now G is isomorphic to C7. In GAP I could check this with the StructureDescription command, how can I check this in Sage?

Answer 1

This works:

sage: G.as_permutation_group().structure_description()
'C7'

The function should probably be exposed in G directly, however.

Nathann

Answer 2

( I needed this answer -badly-, kept trying all day, got the answer now. ) Sage has no implementation of its own of StructureDescription so GAP must be used. ( I don't know how it works internally but this command gives the required result.

  G.gap().StructureDescription()

Answer 3

It turns out that one can try to convert such finitely presented groups into permutation groups, at which point one can compare them to most "standard" finite groups (using Gap behind the scenes).

sage: H = CyclicPermutationGroup(7)
sage: H.is_isomorphic(G.as_permutation_group())
True