For g ∈ ℤ, let g̅ ∈ ℤ8 denote the residue class of g modulo 8. Consider the group \(\mathbb{Z}_8^{\times}\) = {x̅ ∈ ℤ8 : 1 ≤ x ≤ 7, gcd(x, 8) = 1} with respect to multiplication modulo 8. The number of group isomorphisms from \(\mathbb{Z}_8^{\times}\) onto itself is equal to ___________.
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