diff --git a/lmfdb/api/api.py b/lmfdb/api/api.py
index 53d9e4071a..198316b18e 100644
--- a/lmfdb/api/api.py
+++ b/lmfdb/api/api.py
@@ -388,7 +388,7 @@ def apierror(msg, flash_extras=[], code=404, table=False):
     search_schema = {}
     extra_schema = {}
     for label, table, col, sort in zip(labels, tables, label_cols, sorts):
-        if type(col) == list:  # Needed for gps_conj_classes, which effectively has a pair of columns for a label
+        if isinstance(col, list):  # Needed for gps_conj_classes, which effectively has a pair of columns for a label
             q = dict(zip(col, label))
         else:
             q = {col: label}
diff --git a/lmfdb/groups/abstract/main.py b/lmfdb/groups/abstract/main.py
index 8234d2c21f..c63d0ab550 100644
--- a/lmfdb/groups/abstract/main.py
+++ b/lmfdb/groups/abstract/main.py
@@ -147,7 +147,6 @@ def label_is_valid(lab):
     return abstract_group_label_regex.fullmatch(lab)
 
 
-
 #parser for conjugacy class search
 @search_parser(clean_info=True, prep_ranges=True)
 def parse_group(inp, query, qfield):
@@ -1252,7 +1251,7 @@ def indicator_type(strg):
     strg = strg.replace("S","-1")
     return strg
 
-def char_to_sub(short_label, group, as_latex = None):
+def char_to_sub(short_label, group, as_latex=None):
     if short_label:
         full_label = f"{group}.{short_label}"
         if as_latex:
@@ -1333,23 +1332,22 @@ def complex_char_search(info, query={}):
 #    parse_regex_restricted(info, query, "kernel", regex=abstract_group_label_regex)
 
 
-
 #need mathmode for MultiProcessedCol
-def cc_repr(label,code , latex = True):  #default is include dollar signs
+def cc_repr(label,code , latex=True):  #default is include dollar signs
     gp = WebAbstractGroup(label)
     if gp.representations.get("Lie") and gp.representations["Lie"][0]["family"][0] == "P" and gp.order < 2000:
         return ""   #Problem with PGL, PSL, etc
     if latex:
-        return "$" + gp.decode(code,as_str= True) + "$"
+        return "$" + gp.decode(code,as_str=True) + "$"
     else:  # this is for download postprocess
         if gp.element_repr_type == "Perm" or gp.element_repr_type == "PC":
-            return gp.decode(code,as_str= True)
+            return gp.decode(code,as_str=True)
         else:   # matrices as lists
-            return gp.decode(code,as_str= False)
+            return gp.decode(code,as_str=False)
 
 def Power_col(i, ps):
     p = ps[i]
-    return MultiProcessedCol("power_cols", None, f"{p}P", ["group_order", "group_counter", "powers","highlight_col"], lambda group_order, group_counter,  powers, highlight_col: get_cc_url(group_order, group_counter, powers[i], highlight_col), align="center")
+    return MultiProcessedCol("power_cols", None, f"{p}P", ["group_order", "group_counter", "powers","highlight_col"], lambda group_order, group_counter, powers, highlight_col: get_cc_url(group_order, group_counter, powers[i], highlight_col), align="center")
 
 
 def gp_link(gp_order,gp_counter, tex_cache):
@@ -1357,7 +1355,7 @@ def gp_link(gp_order,gp_counter, tex_cache):
     return display_url_cache(gp, tex_cache)
 
 conjugacy_class_columns = SearchColumns([
-    MultiProcessedCol("group", "group.name", "Group", ["group_order", "group_counter", "tex_cache"], gp_link, apply_download=lambda group_order, group_counter, tex_cache: cc_data_to_gp_label(group_order, group_counter)), 
+    MultiProcessedCol("group", "group.name", "Group", ["group_order", "group_counter", "tex_cache"], gp_link, apply_download=lambda group_order, group_counter, tex_cache: cc_data_to_gp_label(group_order, group_counter)),
     MultiProcessedCol("label", "group.label_conjugacy_class", "Label",["group_order", "group_counter", "label","highlight_col"],get_cc_url, download_col="label"),
     MathCol("order", "group.order_conjugacy_class", "Order"),
     MathCol("size", "group.size_conjugacy_class", "Size"),
@@ -1423,7 +1421,7 @@ def cc_postprocess(res, info, query):
         else:
             highlight_col[(group, label)] = None
     if missing:
-        for rec in db.gps_conj_classes.search({"$or":[{"group_order":group_order,"group_counter":group_counter, "counter":{"$in":counters}} for ((group_order,group_counter), counters) in missing.items()]}, ["group_order", "group_counter",  "counter", "label"]):
+        for rec in db.gps_conj_classes.search({"$or":[{"group_order":group_order,"group_counter":group_counter, "counter":{"$in":counters}} for ((group_order,group_counter), counters) in missing.items()]}, ["group_order", "group_counter", "counter", "label"]):
             gp_ord = rec.get("group_order")
             gp_counter = rec.get("group_counter")
             group = cc_data_to_gp_label(gp_ord,gp_counter)
@@ -1695,7 +1693,6 @@ def render_abstract_subgroup(label):
 
     bread = get_bread([(label,)])
 
-
     return render_template(
         "abstract-show-subgroup.html",
         title=title,
@@ -1871,8 +1868,8 @@ def gp_data(label):
     if group_counter.isdigit():
         group_counter = int(group_counter)
     else:
-        group_counter = class_to_int(group_counter) + 1  # we start labeling at 1   
-    return datapage([label, [group_order, group_counter], label, label, label], ["gps_groups", "gps_conj_classes", "gps_qchar", "gps_char", "gps_subgroups"], bread=bread, title=title, label_cols=["label", ["group_order","group_counter"], "group", "group", "ambient"])  
+        group_counter = class_to_int(group_counter) + 1  # we start labeling at 1
+    return datapage([label, [group_order, group_counter], label, label, label], ["gps_groups", "gps_conj_classes", "gps_qchar", "gps_char", "gps_subgroups"], bread=bread, title=title, label_cols=["label", ["group_order","group_counter"], "group", "group", "ambient"])
 
 @abstract_page.route("/sdata/<label>")
 def sgp_data(label):
@@ -2736,7 +2733,6 @@ def cc_data(gp, label, typ="complex", representative=None):
             sub_display_knowl(centralizer, "$" + wcent.subgroup_tex + "$")
         )
 
-
     if representative:
         ans += "<br>Representative: "+representative
     elif wacc.representative is None:
diff --git a/lmfdb/groups/abstract/test_browse_page.py b/lmfdb/groups/abstract/test_browse_page.py
index da9c669491..bf22740697 100644
--- a/lmfdb/groups/abstract/test_browse_page.py
+++ b/lmfdb/groups/abstract/test_browse_page.py
@@ -579,8 +579,8 @@ def test_conj_class_search(self):
         """
         self.check_args("/Groups/Abstract/?group=12.4&search_type=ConjugacyClasses", ["3.a1.a1", "6A"])
         self.check_args("/Groups/Abstract/?group=128.15&search_type=ConjugacyClasses", r"\OD_{16}:C_8" #group name
-        )        
-        
+        )
+
     def test_highlighted_conj_class(self):
         r"""
         Check that conjugacy class links work
diff --git a/lmfdb/groups/abstract/web_groups.py b/lmfdb/groups/abstract/web_groups.py
index b509b1db32..18a117185d 100644
--- a/lmfdb/groups/abstract/web_groups.py
+++ b/lmfdb/groups/abstract/web_groups.py
@@ -98,7 +98,7 @@ def group_pretty_image(label):
 
 
 # Functions below are for conjugacy class searches
-def gp_label_to_cc_data(gp): 
+def gp_label_to_cc_data(gp):
     gp_ord, gp_counter = gp.split(".")
     gp_order = int(gp_ord)
     if re.fullmatch(r'\d+',gp_counter):
@@ -110,19 +110,19 @@ def gp_label_to_cc_data(gp):
 def in_small_gp_db(order):
     if order == 1024:
         return False
-    if order <= 2000  or  order in {2187, 6561, 3125, 2401}:
+    if order <= 2000 or order in {2187, 6561, 3125, 2401}:
         return True
     f = factor(order)
     if all(f[i][1] == 1 and f[i][0] < 1073741824 for i in range(len(f))):
-        return True     
+        return True
     if len(f) == 2:
         pairs, n = exists((i for i in {0,1}), lambda i: f[i][1] == 1)
         if pairs:
-            p = f[1-n] 
-            if ( p[1] <= 2 or p[0] == 2  and  p[1] <= 8
-                  or p[0] == 3  and  p[1] <= 6
-                  or p[0] == 5  and  p[1] <= 5
-                  or p[0] == 7  and  p[1] <= 4 ):
+            p = f[1-n]
+            if ( p[1] <= 2 or p[0] == 2 and p[1] <= 8
+                  or p[0] == 3 and p[1] <= 6
+                  or p[0] == 5 and p[1] <= 5
+                  or p[0] == 7 and p[1] <= 4 ):
                 return True
     if len(f) <= 3 and sum([p[1] for p in f]) == 4:
         return True
@@ -134,9 +134,9 @@ def in_small_gp_db(order):
 def cc_data_to_gp_label(order,counter):
     if in_small_gp_db(order):
         return str(order) + '.' + str(counter)
-    return str(order) + '.' + cremona_letter_code(counter-1)  
+    return str(order) + '.' + cremona_letter_code(counter-1)
+
 
-    
 @cached_function(key=lambda label,name,pretty,ambient,aut,profiledata,cache: (label,name,pretty,ambient,aut,profiledata))
 def abstract_group_display_knowl(label, name=None, pretty=True, ambient=None, aut=False, profiledata=None, cache={}):
     # If you have the group in hand, set the name using gp.tex_name since that will avoid a database call
@@ -612,7 +612,6 @@ def cc_known(self):
 #            return False   # problem with PGL, PSL, etc.
         return db.gps_conj_classes.exists({'group_order': self.order, 'group_counter': self.counter})
 
-    
     @lazy_attribute
     def element_repr_type(self):
         if isinstance(self._data, (tuple, list)) and self.solvable:
@@ -1369,7 +1368,7 @@ def conjugacy_classes(self):
             return cl
         cl = [
             WebAbstractConjClass(self.label, ccdata["label"], ccdata)
-            for ccdata in db.gps_conj_classes.search({"group_order": self.order, "group_counter": self.counter}) 
+            for ccdata in db.gps_conj_classes.search({"group_order": self.order, "group_counter": self.counter})
         ]
         divs = defaultdict(list)
         autjs = defaultdict(list)
@@ -2119,7 +2118,7 @@ def representation_line(self, rep_type, skip_head=False):
                 pres = " $" + pres + "$"
             if self.abelian and not self.cyclic:
                 if skip_head:
-                    pres = " of the abelian group " + pres 
+                    pres = " of the abelian group " + pres
                 else:
                     pres = "Abelian group " + pres
             if skip_head:
@@ -2515,7 +2514,7 @@ def repr_strg(self, other_page=False):
             return f"Elements of the group are displayed as permutations of degree {d}."
         elif rep_type == "PC":
             rep_str =  "Elements of the group are displayed as words in the presentation"
-            if other_page: 
+            if other_page:
                 return rep_str + self.representation_line("PC", skip_head=True)
             else:
                 return rep_str + " generators from the presentation above."
@@ -3073,11 +3072,11 @@ def thesocle(self):
 
 # Conjugacy class labels do not contain the group
 class WebAbstractConjClass(WebObj):
-    table = db.gps_conj_classes 
+    table = db.gps_conj_classes
     def __init__(self, group, label, data=None):
         if data is None:
             group_order, group_counter = gp_label_to_cc_data(group)
-            data = db.gps_conj_classes.lucky({"group_order": group_order, "group_counter" : group_counter, "label": label}) 
+            data = db.gps_conj_classes.lucky({"group_order": group_order, "group_counter" : group_counter, "label": label})
         WebObj.__init__(self, label, data)
         self.force_repr_elt = False