order  association schemes  finite groups  primitive  noncommutative  non Schurian  character
tables 

1  1  1  1  0 
0  
2  1  1  1  0 
0  
3  2  1  2  0 
0  order 3 to 10 
4  4  2  1  0 
0  
5  3  1  3  0 
0  
6  8  2  1  1 
0  
7  4  1  4  0 
0  
8  21  5  1  2 
0 

9  12  2  2  0 
0  
10  13  2  2  2 
0 

11  4  1  4  0 
0  same as Schurian 
12  59  5  1  12 
0 
order 12 
13  6  1  6  0 
0  same as Schurian 
14  16  2  1  2 
0  order 14, 15 
15  25  1  3  1 
1  
16  222  14  6  49 
16 
order 16 
17  5  1  5  0 
0 
same as Schurian 
18  95  5  1  22 
2 
order 18 
19  7  1  7  0 
1 
same as Schurian 
20  95  5  1  22 
0 
order 20 
21  32  2  3  3 
0 
order 21 
22  16  2  1  2 
0 
order 22 
23  22  1  22  0 
18 
same as Schurian 
24  750  15  1  242 
81 
order 24 
25  45  2  16  0 
13 
order 25 
26  34  2  11  4 
10 
order 26 
27  502  5  378  10 
380 
order 27 
28  185  4  8  22 
61 
order 28 
29  26  1  26  0 
20 
same as Schurian 
30  243  4  1  66 
15 
order 30 
31 
? 
1 
0 
same as
Schurian 

32  18210  51  1  3581 
13949 
computed 
33  27  1  1  0 
0 
computed 
34  20  2  1  4 
0 
computed 
35 
? 
1 

36 
? 
14 

37 
? 
1 
0 
same as Schurian  
38  33  2  1  4 
11 
computed 
39 
? 
2 

40 
? 
14 
Note that we omit thin schemes (finite groups) in our data.
Our association schemes are same as
homogeneous coherent configurations.
The newest result is the classification of all
association schemes of order
34 (2003 Oct 15).
These results were calculated by GAP
and an original program written in
C language.