[...] > > And finally for those groups who are not known to gap, the fallback > > (sage-only) method should be in the category FiniteGroups to be inherited by > > any group. > > I hadn't thought of that. Since all the groups I used are defined as > permutation groups I never ran into trouble, but now that you mention > it I see that GAP function doesn't work for matrix groups: No, that's not true. It must be a bug or a feature of Sage, not something that does not work in GAP. Here is the GAP session that does what you tried below:
gap> a1:=Z(5)^0*[[1,2],[-1,-1]]; [ [ Z(5)^0, Z(5) ], [ Z(5)^2, Z(5)^2 ] ] gap> a2:=Z(5)^0*[[1,1],[0,1]]; [ [ Z(5)^0, Z(5)^0 ], [ 0*Z(5), Z(5)^0 ] ] gap> gg:=Group(a1,a2); Group([ [ [ Z(5)^0, Z(5) ], [ Z(5)^2, Z(5)^2 ] ], [ [ Z(5)^0, Z(5)^0 ], [ 0*Z(5), Z(5)^0 ] ] ]) gap> ConjugacyClass(gg,a1); [ [ Z(5)^0, Z(5) ], [ Z(5)^2, Z(5)^2 ] ]^G > > sage: F = GF(5) > sage: gens = [matrix(F,2,[1,2, -1, 1]), matrix(F,2, [1,1, 0,1])] > sage: G = MatrixGroup(gens) > sage: g = G(matrix(F,2,[1,2, -1, 1])) > sage: conjugacy_class_gap(g,G) > Traceback (most recent call last): > ... > NotImplementedError > [...] HTH, Dmitrii
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