The following code shows that subgroups of automorphism groups of graphs 
are handled wrongly:

sage: g = Graph([[1, 2, 4], []])
sage: a = g.automorphism_group()
sage: print(a)
Permutation Group with generators [(2,4), (1,2)]
sage: print(a.commutator())
Permutation Group with generators [(1,2,3)]

Note that  a.commutator() moves 3 though 3 is not a vertex of the graph. 
Somewhat strangely, if one defines directly a = PermutationGroup([[(2, 4)], 
[(1, 2)]]), then a.commutator() returns the correct subgroup.

By the way, it doesn't help if the n vertices of the graph consist of the 
list [1..n]. I have a complicated example where the automorphism group is 
computed correctly, but the action of the commutator subgroup is with 
respect to a different labeling of the vertices.

-- Peter Mueller

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