| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 1 | 12 | 17 | 0 | 11 | 16 | 13 | 10 | 15 | 14 | 8 | 4 | 2 | 6 | 7 | 9 | 5 | 3 |
| 2 | 17 | 0 | 12 | 13 | 11 | 16 | 14 | 10 | 15 | 7 | 6 | 3 | 5 | 9 | 8 | 4 | 1 |
| 3 | 0 | 12 | 17 | 16 | 13 | 11 | 15 | 14 | 10 | 9 | 5 | 1 | 4 | 8 | 7 | 6 | 2 |
| 4 | 15 | 10 | 14 | 17 | 12 | 0 | 11 | 16 | 13 | 1 | 8 | 6 | 7 | 2 | 3 | 9 | 5 |
| 5 | 14 | 15 | 10 | 12 | 0 | 17 | 16 | 13 | 11 | 3 | 9 | 4 | 8 | 1 | 2 | 7 | 6 |
| 6 | 10 | 14 | 15 | 0 | 17 | 12 | 13 | 11 | 16 | 2 | 7 | 5 | 9 | 3 | 1 | 8 | 4 |
| 7 | 13 | 16 | 11 | 15 | 14 | 10 | 12 | 0 | 17 | 6 | 2 | 9 | 3 | 5 | 4 | 1 | 8 |
| 8 | 11 | 13 | 16 | 14 | 10 | 15 | 0 | 17 | 12 | 4 | 1 | 7 | 2 | 6 | 5 | 3 | 9 |
| 9 | 16 | 11 | 13 | 10 | 15 | 14 | 17 | 12 | 0 | 5 | 3 | 8 | 1 | 4 | 6 | 2 | 7 |
| 10 | 5 | 4 | 6 | 7 | 8 | 9 | 2 | 1 | 3 | 11 | 0 | 14 | 12 | 13 | 16 | 17 | 15 |
| 11 | 7 | 9 | 8 | 3 | 2 | 1 | 6 | 4 | 5 | 0 | 10 | 13 | 14 | 12 | 17 | 15 | 16 |
| 12 | 2 | 3 | 1 | 6 | 4 | 5 | 9 | 7 | 8 | 14 | 13 | 17 | 16 | 15 | 10 | 11 | 0 |
| 13 | 9 | 8 | 7 | 1 | 3 | 2 | 5 | 6 | 4 | 12 | 14 | 16 | 15 | 17 | 0 | 10 | 11 |
| 14 | 4 | 6 | 5 | 9 | 7 | 8 | 3 | 2 | 1 | 13 | 12 | 15 | 17 | 16 | 11 | 0 | 10 |
| 15 | 6 | 5 | 4 | 8 | 9 | 7 | 1 | 3 | 2 | 16 | 17 | 10 | 0 | 11 | 13 | 12 | 14 |
| 16 | 8 | 7 | 9 | 2 | 1 | 3 | 4 | 5 | 6 | 17 | 15 | 11 | 10 | 0 | 12 | 14 | 13 |
| 17 | 3 | 1 | 2 | 5 | 6 | 4 | 8 | 9 | 7 | 15 | 16 | 0 | 11 | 10 | 14 | 13 | 12 |
Centre: 0 12 17
Centrum: 0 12 17
Nucleus: 0 12 17
Left Nucleus: 0 4 5 6 12 17
Middle Nucleus: 0 12 17
Right Nucleus: 0 12 17
1 Element of order 1: 0
3 Elements of order 2: 2 5 9
8 Elements of order 3: 10 11 12 13 14 15 16 17
6 Elements of order 6: 1 3 4 6 7 8
Commutator Subloop: 0 10 11 12 13 14 15 16 17
Associator Subloop: 0 12 17
3 Conjugacy Classes of size 1:
1 Conjugacy Class of size 6:
1 Conjugacy Class of size 9:
Automorphic Inverse Property: FAILS. (1-1)(5-1) neq (1*5)-1
Al Property: FAILS. The left inner mapping L1,1 = (4,5,6)(7,9,8)(10,14,15)(11,16,13) is not an automorphism. L1,1(4*1) neq L1,1(4)*L1,1(1)
Ar Property: FAILS. The right inner mapping R1,4 = (1,2,3)(7,8,9)(10,14,15)(11,16,13) is not an automorphism. R1,4(1*1) neq R1,4(1)*R1,4(1)
Right (Left, Full) Mult Group Orders: 54 (162, 972)
/ revised November, 2001