diff --git a/src/sage/groups/perm_gps/permgroup_named.py b/src/sage/groups/perm_gps/permgroup_named.py
index 5c153b93d4c..f3ab6891559 100644
--- a/src/sage/groups/perm_gps/permgroup_named.py
+++ b/src/sage/groups/perm_gps/permgroup_named.py
@@ -2725,7 +2725,8 @@ def __init__(self, n, q, name='a'):
         """
         from sage.categories.finite_fields import FiniteFields
         if q in FiniteFields():
-            name = q.gen()
+            if q.degree() > 1:
+                name = q.gen()
             q = q.cardinality()
         if q not in NonNegativeIntegers():
             raise ValueError('q must be a prime power or a finite field')