Steps To Reproduce

F.<x,y> = FreeGroup()
G = F / [x^4, y^13, x*y*x^-1*y^-5]
a, b = G.gens()
assert(G.order() == 52)
assert(a.order() == 4)
assert(b.order() == 13)
assert(a*b*a^-1 == b^5) # isomorphic to semidirect product of Z_4 and Z_13
gr = G.cayley_graph(generators=[a,b]).to_undirected()
print(gr.num_verts()) # prints 109

Expected Behavior

The Cayley graph of a group with 52 elements should have 52 vertices.

Actual Behavior

The Cayley graph has 109 vertices.

Additional Information

The issue disappears if one converts the group to a permutation group.

Environment

• OS: Arch Linux
• Sage Version: 10.6-6

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide