| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 1 | 2 | 3 | 0 | 5 | 7 | 4 | 6 | 9 | 11 | 8 | 10 | 13 | 14 | 15 | 12 |
| 2 | 3 | 0 | 1 | 7 | 6 | 5 | 4 | 11 | 10 | 9 | 8 | 14 | 15 | 12 | 13 |
| 3 | 0 | 1 | 2 | 6 | 4 | 7 | 5 | 10 | 8 | 11 | 9 | 15 | 12 | 13 | 14 |
| 4 | 5 | 7 | 6 | 0 | 1 | 3 | 2 | 12 | 15 | 13 | 14 | 8 | 10 | 11 | 9 |
| 5 | 7 | 6 | 4 | 1 | 2 | 0 | 3 | 15 | 14 | 12 | 13 | 10 | 11 | 9 | 8 |
| 6 | 4 | 5 | 7 | 3 | 0 | 2 | 1 | 13 | 12 | 14 | 15 | 9 | 8 | 10 | 11 |
| 7 | 6 | 4 | 5 | 2 | 3 | 1 | 0 | 14 | 13 | 15 | 12 | 11 | 9 | 8 | 10 |
| 8 | 9 | 11 | 10 | 12 | 15 | 13 | 14 | 3 | 0 | 2 | 1 | 7 | 5 | 4 | 6 |
| 9 | 11 | 10 | 8 | 15 | 14 | 12 | 13 | 0 | 1 | 3 | 2 | 5 | 4 | 6 | 7 |
| 10 | 8 | 9 | 11 | 13 | 12 | 14 | 15 | 2 | 3 | 1 | 0 | 6 | 7 | 5 | 4 |
| 11 | 10 | 8 | 9 | 14 | 13 | 15 | 12 | 1 | 2 | 0 | 3 | 4 | 6 | 7 | 5 |
| 12 | 15 | 14 | 13 | 8 | 9 | 10 | 11 | 6 | 4 | 7 | 5 | 2 | 1 | 0 | 3 |
| 13 | 12 | 15 | 14 | 10 | 8 | 11 | 9 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 14 | 13 | 12 | 15 | 11 | 10 | 9 | 8 | 5 | 7 | 4 | 6 | 0 | 3 | 2 | 1 |
| 15 | 14 | 13 | 12 | 9 | 11 | 8 | 10 | 4 | 5 | 6 | 7 | 1 | 0 | 3 | 2 |
Centre: 0 2
Centrum: 0 2 4 7
Nucleus: 0 2
Left Nucleus: 0 2 4 7
Middle Nucleus: 0 1 2 3
Right Nucleus: 0 1 2 3
1 Element of order 1: 0
3 Elements of order 2: 2 4 7
8 Elements of order 4: 1 3 5 6 12 13 14 15
4 Elements of order 8: 8 9 10 11
Commutator Subloop: 0 1 2 3
Associator Subloop: 0 1 2 3
2 Conjugacy Classes of size 1:
3 Conjugacy Classes of size 2:
2 Conjugacy Classes of size 4:
Automorphic Inverse Property: FAILS. (1-1)(13-1) neq (1*13)-1
Al Property: FAILS. The left inner mapping L4,8 = (8,10,11,9)(12,15,14,13) is not an automorphism. L4,8(4*8) neq L4,8(4)*L4,8(8)
Ar Property: HOLDS (i.e. every right inner mapping Ra,b is an automorphism)
Right (Left, Full) Mult Group Orders: 32 (512, 2048)
/ revised October, 2001