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I would like to work with the group $\mathbb{Z}_m^* / \langle p \rangle$. Do you know how I can create it?

For example:

p = 2
m = 17^2
Zm = ZZ.quotient(m)  # ring of integers mod m
Zms = Zm.unit_group() # cyclic group (Z/mZ)^* generated by 3
Zms.quotient(p)

But the last line raises a NotImplementedError.