Note that, if there exists an association scheme of prime order p and class d, then d must be a divisor of p-1.

Order 50
Class # isomorphism classes date machine character tables
1 1 -- -- --
2
3
4
5
6
7 (3 days on kissme, 2008/07)
8 17 (2009/07/15) (Core2Quad:090703) computed
9 (3 days on kissme, 2008/07)
10 11 (2009/07/03) (Core2Quad:090703) computed
11 28 (2009/07/08) (Core2Quad:090703) computed
12 0 (2009/07/08) (Core2Quad:090703) ---
13 35 (2009/07/12) (Core2Quad:090703) computed
14 4 (2009/07/12) (Core2Quad:090703) computed
15 (7 days on Core2Quad, 2010/06)
16 0 (2009/07/15) (Core2Quad:090703) ---
17 (16 days on kissme, 2008/08)
18 0 2009/07/16 Core2Quad:090703 ---
19 5 2009/07/16 Core2Quad:090703 computed
20 0 2009/07/17 Core2Quad:090703 ---
21 0 2010/08/31 Core2Quad:090723 ---
22 0 2009/09/19 Core2Quad:090723 ---
23
24
25
26 -- 28 0 (2009/08/29) (Core2Quad:090723) --
29 difficult !
30 -- 48 0 (2009/08/29) (Core2Quad:090723) --
49 (thin) 5 -- -- --

Order 51
Class # isomorphism classes date machine character tables
1 1 -- -- --
7 1 2018/03/13 -- --
8 1 2018/02/28 -- --
9 3 2018/03/01 -- --
11 0 2010/11/12 Core2Quad:20090723 --
12
13 1 2010/09/10 Core2Quad:20090723 computed
14 1 2010/09/06 Core2Quad:20090723 computed
15 -- 16 0 2010/09/07 Core2Quad:20090723 --
17 3 2010/09/07 Core2Quad:20090723 computed
18 2 2010/09/07 Core2Quad:20090723 computed
19 0 2010/09/07 Core2Quad:20090723 --
20 0 2010/09/09 Core2Quad:20090723 --
21 0 2010/09/10 Core(TM)i7:20090723 --
23 0 2010/10/23 Core2Quad:20090723 --
24 0 2010/10/24 Core2Quad:20090723 --
26 1 2010/11/03 Core2Quad:20090723 computed
27 -- 32 0 2010/09/08 Core2Quad:20090723 --
33
34 -- 49 0 2010/09/06 Core2Quad:20090723 --
50 (thin) 1 -- -- --

Order 52
Class # isomorphism classes date machine character tables
1 1 -- -- --
10 6 2010/10/14 Core2Quad:20090723 computed
11 13 2010/10/13 Core2Quad:20090723 computed
12 0 2010/10/10 Core2Quad:20090723 --
13 3 2010/10/10 Core2Quad:20090723 computed
18 0 2010/09/15 Core2Quad:20090723 --
19 5 2010/09/18 Core2Quad:20090723 computed
20 2 2010/09/20 Core2Quad:20090723 computed
21 2 2010/09/25 Core2Quad:20090723 computed
22 0 2010/09/25 Core2Quad:20090723 --
23 0 2010/10/06 Core2Quad:20090723 --
24 0 2010/10/10 Core2Quad:20090723 --
30 -- 37 0 2010/09/08 Core2Quad:20090723 --
38
39 -- 50 0 2010/09/06 Core2Quad:20090723 --
51 (thin) 5 -- -- --

Order 53
Class Number of isomorphism classes date machine character tables
1
1
-- -- --
2
4
13
(7 days on Core2Quad 2009/10)
26
1 (Schurian) -- -- --
52 (thin)
1 -- -- --

Order 54
Class # isomorphism classes date machine character tables
1 1 -- -- --
2 6 SRG on (prime + 1) points
17 112 2012/11/13 Core2Quad:20121109 computed
18 27 2012/11/12 Core2Quad:20121109 computed
20 35 2010/10/13 Core2Quad:20090723 computed
21 72 2010/10/18 Core2Quad:20090723 computed
36 -- 39 0 2010/09/08 Core2Quad:20090723 --
40
41 -- 52 0 2010/09/06 Core2Quad:20090723 --
53 (thin) 15 -- -- --

Order 55
Class # isomorphism classes date machine character tables
1 1 -- -- --
10 0 2018/02/21 -- --
14 3 2012/12/05 Core2Quad:20121109 computed
19 0 2012/11/16 Core2Quad:20121109 --
20 0 2012/11/16 Core2Quad:20121109 --
21 1 2012/11/16 Core2Quad:20121109 --
22 0 2012/11/10 Core2Quad:20121109 --
23 0 2012/11/12 Core2Quad:20121109 --
24 0 2012/11/13 Core2Quad:20121109 --
25 0 2012/11/14 Core2Quad:20121109 --
26 0 2012/11/15 Core2Quad:20121109 --
30, 31 0 2010/09/13 Core(TM)i7:20090723 --
32
33 -- 53 0 2010/09/06 Core2Quad:20090723 --
54 (thin) 2 -- -- --

Order 56
Class # isomorphism classes date machine character tables
1 1 -- -- --
20 3 2018/03/09 -- --
42 -- 54 0 2010/09/13 Core(TM)i7:20090723 --
55 (thin) 13 -- -- --

Order 57
Class # isomorphism classes date machine character tables
1 1 -- -- --
30 -- 36 0 2010/09/13 Core(TM)i7:20090723 --
37
38 -- 55 0 2010/09/13 Core(TM)i7:20090723 --
56 (thin) 2 -- -- --

Order 58
Class # isomorphism classes date machine character tables
1 1 -- -- --
30 -- 56 0 2018/02/11 -- --
57 (thin) 2 -- -- --

Order 59
Class # isomorphism classes date machine character tables
1 1 -- -- --
2 -- -- -- --
29 1 -- -- --
58 (thin) 1 -- -- --