My goal is to aggregate a pandas DataFrame, grouping rows by an identity field. Notably, rather than just gathering summary statistics of the group, I want to retain all the information in the DataFrame in addition to summary statistics like mean, std, etc. I have performed this transformation via a lot of iteration, but I am looking for a cleaner/more pythonic approach. Notably, there may be more or less than 2 replicates per group, but all groups will always have the same number of replicates.
Example: I would llke to translate the below format
df = pd.DataFrame([
    ["group1", 4, 10],
    ["group1", 8, 20],
    ["group2", 6, 30],
    ["group2", 12, 40],
    ["group3", 1, 50],
    ["group3", 3, 60]], 
  columns=['group','timeA', 'timeB'])
print(df)
    group  timeA  timeB
0  group1      4     10
1  group1      8     20
2  group2      6     30
3  group2     12     40
4  group3      1     50
5  group3      3     60
into a df of the following format:
target = pd.DataFrame([
    ["group1", 4, 8, 6, 10, 20, 15],
    ["group2", 6, 12, 9, 30, 45, 35],
    ["group3", 1, 3, 2, 50, 60, 55]
], columns = ["group", "timeA.1", "timeA.2", "timeA.mean", "timeB.1", "timeB.2", "timeB.mean"])
print(target)
    group  timeA.1  timeA.2  timeA.mean  timeB.1  timeB.2  timeB.mean
0  group1        4        8           6       10       20          15
1  group2        6       12           9       30       45          35
2  group3        1        3           2       50       60          55
Finally, it doesn't really matter what the column names are, these ones are just to make the example more clear. Thanks!
EDIT: As suggested by a user in the comments, I tried the solution from the linked Q/A without success:
df.insert(0, 'count', df.groupby('group').cumcount())
df.pivot(*df)
TypeError: pivot() takes from 1 to 4 positional arguments but 5 were given
 
    