| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 1 | 5 | 7 | 6 | 0 | 2 | 4 | 3 |
| 2 | 7 | 6 | 0 | 5 | 3 | 1 | 4 |
| 3 | 6 | 0 | 5 | 7 | 4 | 2 | 1 |
| 4 | 0 | 5 | 7 | 6 | 1 | 3 | 2 |
| 5 | 2 | 3 | 4 | 1 | 7 | 0 | 6 |
| 6 | 4 | 1 | 2 | 3 | 0 | 7 | 5 |
| 7 | 3 | 4 | 1 | 2 | 6 | 5 | 0 |
Centre: 0 1 2 3 4 5 6 7
Centrum: 0 1 2 3 4 5 6 7
Nucleus: 0 1 2 3 4 5 6 7
Left Nucleus: 0 1 2 3 4 5 6 7
Middle Nucleus: 0 1 2 3 4 5 6 7
Right Nucleus: 0 1 2 3 4 5 6 7
1 Element of order 1: 0
1 Element of order 2: 7
2 Elements of order 4: 5 6
4 Elements of order 8: 1 2 3 4
Commutator Subloop: 0
Associator Subloop: 0
8 Conjugacy Classes of size 1:
Automorphic Inverse Property: HOLDS
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: 8 (8, 8)
/ revised November, 2001