| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 1 | 16 | 19 | 15 | 17 | 18 | 13 | 12 | 0 | 11 | 14 | 5 | 2 | 3 | 4 | 6 | 8 | 10 | 9 | 7 |
| 2 | 15 | 17 | 18 | 16 | 19 | 0 | 11 | 14 | 13 | 12 | 1 | 3 | 4 | 5 | 7 | 9 | 6 | 10 | 8 |
| 3 | 18 | 16 | 19 | 15 | 17 | 14 | 13 | 12 | 0 | 11 | 2 | 4 | 5 | 1 | 8 | 10 | 7 | 6 | 9 |
| 4 | 19 | 15 | 17 | 18 | 16 | 12 | 0 | 11 | 14 | 13 | 3 | 5 | 1 | 2 | 9 | 6 | 8 | 7 | 10 |
| 5 | 17 | 18 | 16 | 19 | 15 | 11 | 14 | 13 | 12 | 0 | 4 | 1 | 2 | 3 | 10 | 7 | 9 | 8 | 6 |
| 6 | 11 | 0 | 12 | 13 | 14 | 17 | 15 | 19 | 16 | 18 | 7 | 10 | 9 | 8 | 1 | 4 | 2 | 3 | 5 |
| 7 | 13 | 14 | 11 | 0 | 12 | 16 | 18 | 17 | 15 | 19 | 8 | 6 | 10 | 9 | 2 | 5 | 3 | 4 | 1 |
| 8 | 0 | 12 | 13 | 14 | 11 | 15 | 19 | 16 | 18 | 17 | 9 | 7 | 6 | 10 | 3 | 1 | 4 | 5 | 2 |
| 9 | 14 | 11 | 0 | 12 | 13 | 18 | 17 | 15 | 19 | 16 | 10 | 8 | 7 | 6 | 4 | 2 | 5 | 1 | 3 |
| 10 | 12 | 13 | 14 | 11 | 0 | 19 | 16 | 18 | 17 | 15 | 6 | 9 | 8 | 7 | 5 | 3 | 1 | 2 | 4 |
| 11 | 4 | 5 | 1 | 2 | 3 | 9 | 10 | 6 | 7 | 8 | 14 | 0 | 12 | 13 | 17 | 19 | 18 | 16 | 15 |
| 12 | 3 | 4 | 5 | 1 | 2 | 8 | 9 | 10 | 6 | 7 | 0 | 13 | 14 | 11 | 19 | 18 | 15 | 17 | 16 |
| 13 | 5 | 1 | 2 | 3 | 4 | 10 | 6 | 7 | 8 | 9 | 12 | 14 | 11 | 0 | 16 | 17 | 19 | 15 | 18 |
| 14 | 2 | 3 | 4 | 5 | 1 | 7 | 8 | 9 | 10 | 6 | 13 | 11 | 0 | 12 | 18 | 15 | 16 | 19 | 17 |
| 15 | 9 | 8 | 7 | 6 | 10 | 4 | 3 | 2 | 1 | 5 | 19 | 17 | 18 | 16 | 0 | 14 | 12 | 13 | 11 |
| 16 | 8 | 7 | 6 | 10 | 9 | 3 | 2 | 1 | 5 | 4 | 18 | 19 | 15 | 17 | 13 | 0 | 14 | 11 | 12 |
| 17 | 7 | 6 | 10 | 9 | 8 | 2 | 1 | 5 | 4 | 3 | 15 | 18 | 16 | 19 | 11 | 13 | 0 | 12 | 14 |
| 18 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 17 | 16 | 19 | 15 | 14 | 12 | 11 | 0 | 13 |
| 19 | 6 | 10 | 9 | 8 | 7 | 1 | 5 | 4 | 3 | 2 | 16 | 15 | 17 | 18 | 12 | 11 | 13 | 14 | 0 |
Centre: 0
Centrum: 0
Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Left Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Middle Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Right Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
1 Element of order 1: 0
5 Elements of order 2: 15 16 17 18 19
10 Elements of order 4: 1 2 3 4 5 6 7 8 9 10
4 Elements of order 5: 11 12 13 14
Commutator Subloop: 0 11 12 13 14
Associator Subloop: 0
1 Conjugacy Class of size 1:
1 Conjugacy Class of size 4:
3 Conjugacy Classes of size 5:
Automorphic Inverse Property: FAILS. (1-1)(3-1) neq (1*3)-1
Al Property: HOLDS (i.e. every left inner mapping La,b is an automorphism)
Ar Property: HOLDS (i.e. every right inner mapping Ra,b is an automorphism)
Right (Left, Full) Mult Group Orders: 20 (20, 400)
/ revised November, 2001