| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 1 | 4 | 0 | 2 | 6 | 3 | 8 | 5 | 9 | 7 | 15 | 16 | 17 | 19 | 18 | 10 | 11 | 12 | 14 | 13 |
| 2 | 0 | 3 | 5 | 1 | 7 | 4 | 9 | 6 | 8 | 17 | 19 | 18 | 15 | 16 | 13 | 14 | 10 | 12 | 11 |
| 3 | 2 | 5 | 7 | 0 | 9 | 1 | 8 | 4 | 6 | 12 | 13 | 14 | 10 | 11 | 19 | 18 | 15 | 17 | 16 |
| 4 | 6 | 1 | 0 | 8 | 2 | 9 | 3 | 7 | 5 | 13 | 14 | 10 | 11 | 12 | 17 | 19 | 18 | 16 | 15 |
| 5 | 3 | 7 | 9 | 2 | 8 | 0 | 6 | 1 | 4 | 18 | 15 | 16 | 17 | 19 | 11 | 12 | 13 | 10 | 14 |
| 6 | 8 | 4 | 1 | 9 | 0 | 7 | 2 | 5 | 3 | 19 | 18 | 15 | 16 | 17 | 12 | 13 | 14 | 11 | 10 |
| 7 | 5 | 9 | 8 | 3 | 6 | 2 | 4 | 0 | 1 | 14 | 10 | 11 | 12 | 13 | 16 | 17 | 19 | 15 | 18 |
| 8 | 9 | 6 | 4 | 7 | 1 | 5 | 0 | 3 | 2 | 11 | 12 | 13 | 14 | 10 | 18 | 15 | 16 | 19 | 17 |
| 9 | 7 | 8 | 6 | 5 | 4 | 3 | 1 | 2 | 0 | 16 | 17 | 19 | 18 | 15 | 14 | 10 | 11 | 13 | 12 |
| 10 | 17 | 15 | 13 | 12 | 19 | 18 | 11 | 14 | 16 | 0 | 7 | 4 | 3 | 8 | 9 | 1 | 5 | 2 | 6 |
| 11 | 19 | 16 | 14 | 13 | 18 | 15 | 12 | 10 | 17 | 8 | 0 | 7 | 4 | 3 | 1 | 5 | 6 | 9 | 2 |
| 12 | 18 | 17 | 10 | 14 | 15 | 16 | 13 | 11 | 19 | 3 | 8 | 0 | 7 | 4 | 5 | 6 | 2 | 1 | 9 |
| 13 | 15 | 19 | 11 | 10 | 16 | 17 | 14 | 12 | 18 | 4 | 3 | 8 | 0 | 7 | 6 | 2 | 9 | 5 | 1 |
| 14 | 16 | 18 | 12 | 11 | 17 | 19 | 10 | 13 | 15 | 7 | 4 | 3 | 8 | 0 | 2 | 9 | 1 | 6 | 5 |
| 15 | 10 | 13 | 19 | 17 | 11 | 12 | 16 | 18 | 14 | 1 | 5 | 6 | 2 | 9 | 8 | 0 | 7 | 3 | 4 |
| 16 | 11 | 14 | 18 | 19 | 12 | 13 | 17 | 15 | 10 | 9 | 1 | 5 | 6 | 2 | 0 | 7 | 4 | 8 | 3 |
| 17 | 12 | 10 | 15 | 18 | 13 | 14 | 19 | 16 | 11 | 2 | 9 | 1 | 5 | 6 | 7 | 4 | 3 | 0 | 8 |
| 18 | 14 | 12 | 17 | 16 | 10 | 11 | 15 | 19 | 13 | 5 | 6 | 2 | 9 | 1 | 3 | 8 | 0 | 4 | 7 |
| 19 | 13 | 11 | 16 | 15 | 14 | 10 | 18 | 17 | 12 | 6 | 2 | 9 | 1 | 5 | 4 | 3 | 8 | 7 | 0 |
Centre: 0
Centrum: 0 9 19
Nucleus: 0
Left Nucleus: 0 9 12 19
Middle Nucleus: 0 3 4 7 8
Right Nucleus: 0 3 4 7 8
1 Element of order 1: 0
7 Elements of order 2: 9 10 11 12 13 14 19
4 Elements of order 5: 3 4 7 8
8 Elements of order 10: 1 2 5 6 15 16 17 18
Commutator Subloop: 0 3 4 7 8
Associator Subloop: 0 3 4 7 8
1 Conjugacy Class of size 1:
2 Conjugacy Classes of size 2:
3 Conjugacy Classes of size 5:
Automorphic Inverse Property: FAILS. (1-1)(11-1) neq (1*11)-1
Al Property: FAILS. The left inner mapping L1,1 = (10,12,14,11,13)(15,19,16,18,17) is not an automorphism. L1,1(1*10) neq L1,1(1)*L1,1(10)
Ar Property: HOLDS (i.e. every right inner mapping Ra,b is an automorphism)
Right (Left, Full) Mult Group Orders: 40 (2500, 5000)
/ revised November, 2001