| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 1 | 0 | 17 | 13 | 10 | 15 | 12 | 11 | 14 | 16 | 4 | 7 | 6 | 3 | 8 | 5 | 9 | 2 |
| 2 | 14 | 0 | 17 | 13 | 10 | 15 | 12 | 16 | 11 | 5 | 9 | 7 | 4 | 1 | 6 | 8 | 3 |
| 3 | 16 | 14 | 0 | 17 | 13 | 10 | 15 | 11 | 12 | 6 | 8 | 9 | 5 | 2 | 7 | 1 | 4 |
| 4 | 11 | 16 | 14 | 0 | 17 | 13 | 10 | 12 | 15 | 7 | 1 | 8 | 6 | 3 | 9 | 2 | 5 |
| 5 | 12 | 11 | 16 | 14 | 0 | 17 | 13 | 15 | 10 | 9 | 2 | 1 | 7 | 4 | 8 | 3 | 6 |
| 6 | 15 | 12 | 11 | 16 | 14 | 0 | 17 | 10 | 13 | 8 | 3 | 2 | 9 | 5 | 1 | 4 | 7 |
| 7 | 10 | 15 | 12 | 11 | 16 | 14 | 0 | 13 | 17 | 1 | 4 | 3 | 8 | 6 | 2 | 5 | 9 |
| 8 | 17 | 13 | 10 | 15 | 12 | 11 | 16 | 0 | 14 | 3 | 6 | 5 | 2 | 9 | 4 | 7 | 1 |
| 9 | 13 | 10 | 15 | 12 | 11 | 16 | 14 | 17 | 0 | 2 | 5 | 4 | 1 | 7 | 3 | 6 | 8 |
| 10 | 7 | 9 | 8 | 1 | 2 | 3 | 4 | 6 | 5 | 11 | 0 | 14 | 12 | 13 | 16 | 17 | 15 |
| 11 | 4 | 5 | 6 | 7 | 9 | 8 | 1 | 3 | 2 | 0 | 10 | 13 | 14 | 12 | 17 | 15 | 16 |
| 12 | 5 | 6 | 7 | 9 | 8 | 1 | 2 | 4 | 3 | 14 | 13 | 17 | 16 | 15 | 0 | 10 | 11 |
| 13 | 9 | 8 | 1 | 2 | 3 | 4 | 5 | 7 | 6 | 12 | 14 | 16 | 15 | 17 | 11 | 0 | 10 |
| 14 | 2 | 3 | 4 | 5 | 6 | 7 | 9 | 1 | 8 | 13 | 12 | 15 | 17 | 16 | 10 | 11 | 0 |
| 15 | 6 | 7 | 9 | 8 | 1 | 2 | 3 | 5 | 4 | 16 | 17 | 0 | 11 | 10 | 14 | 13 | 12 |
| 16 | 3 | 4 | 5 | 6 | 7 | 9 | 8 | 2 | 1 | 17 | 15 | 10 | 0 | 11 | 13 | 12 | 14 |
| 17 | 8 | 1 | 2 | 3 | 4 | 5 | 6 | 9 | 7 | 15 | 16 | 11 | 10 | 0 | 12 | 14 | 13 |
Centre: 0
Centrum: 0
Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Left Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Middle Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Right Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1 Element of order 1: 0
9 Elements of order 2: 1 2 3 4 5 6 7 8 9
2 Elements of order 3: 10 11
6 Elements of order 9: 12 13 14 15 16 17
Commutator Subloop: 0 10 11 12 13 14 15 16 17
Associator Subloop: 0
1 Conjugacy Class of size 1:
4 Conjugacy Classes of size 2:
1 Conjugacy Class of size 9:
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: 18 (18, 324)
/ revised November, 2001