| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 1 | 0 | 3 | 2 | 5 | 4 | 7 | 6 |
| 2 | 3 | 1 | 0 | 6 | 7 | 5 | 4 |
| 3 | 2 | 0 | 1 | 7 | 6 | 4 | 5 |
| 4 | 5 | 7 | 6 | 1 | 0 | 2 | 3 |
| 5 | 4 | 6 | 7 | 0 | 1 | 3 | 2 |
| 6 | 7 | 4 | 5 | 3 | 2 | 1 | 0 |
| 7 | 6 | 5 | 4 | 2 | 3 | 0 | 1 |
Centre: 0 1
Centrum: 0 1
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: 1
6 Elements of order 4: 2 3 4 5 6 7
Commutator Subloop: 0 1
Associator Subloop: 0
2 Conjugacy Classes of size 1:
3 Conjugacy Classes of size 2:
Automorphic Inverse Property: FAILS. (2-1)(5-1) neq (2*5)-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: 8 (8, 32)
/ revised November, 2001