gh-37288: Directly convert PermutationGroup element into sized Permutation
    
This patch fixes #37284 by converting the input into a Permutation class
object if
it is the object of another class.
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URL: #37288
Reported by: Ruchit Jagodara
Reviewer(s): grhkm21, Travis Scrimshaw

Author: Release Manager

src/sage/combinat/permutation.py

@@ -7092,7 +7092,19 @@ def _element_constructor_(self, x, check=True):
             [1, 4, 5, 2, 3, 6]
             sage: Permutations(6)(x)            # known bug
             [1, 4, 5, 2, 3, 6]
+
+        Ensure that :issue:`37284` is fixed::
+
+            sage: PG = PermutationGroup([[(1,2,3),(5,6)],[(7,8)]])
+            sage: P8 = Permutations(8)
+            sage: p = PG.an_element()
+            sage: q = P8(p); q
+            [2, 3, 1, 4, 6, 5, 8, 7]
+            sage: q.parent()
+            Standard permutations of 8
         """
+        if isinstance(x, PermutationGroupElement):
+            return self. _from_permutation_group_element(x)
         if len(x) < self.n:
             x = list(x) + list(range(len(x) + 1, self.n + 1))
         return self.element_class(self, x, check=check)