| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 1 | 0 | 15 | 10 | 11 | 13 | 14 | 9 | 12 | 2 | 6 | 5 | 8 | 4 | 3 | 7 |
| 2 | 9 | 12 | 11 | 10 | 14 | 13 | 0 | 15 | 1 | 5 | 6 | 7 | 3 | 4 | 8 |
| 3 | 10 | 13 | 12 | 15 | 9 | 0 | 11 | 14 | 4 | 1 | 2 | 6 | 7 | 8 | 5 |
| 4 | 11 | 14 | 15 | 12 | 0 | 9 | 10 | 13 | 3 | 2 | 1 | 5 | 8 | 7 | 6 |
| 5 | 13 | 10 | 9 | 0 | 12 | 15 | 14 | 11 | 6 | 7 | 8 | 4 | 1 | 2 | 3 |
| 6 | 14 | 11 | 0 | 9 | 15 | 12 | 13 | 10 | 5 | 8 | 7 | 3 | 2 | 1 | 4 |
| 7 | 15 | 0 | 13 | 14 | 10 | 11 | 12 | 9 | 8 | 4 | 3 | 2 | 6 | 5 | 1 |
| 8 | 12 | 9 | 14 | 13 | 11 | 10 | 15 | 0 | 7 | 3 | 4 | 1 | 5 | 6 | 2 |
| 9 | 2 | 1 | 4 | 3 | 6 | 5 | 8 | 7 | 0 | 11 | 10 | 15 | 14 | 13 | 12 |
| 10 | 3 | 4 | 8 | 7 | 2 | 1 | 5 | 6 | 11 | 12 | 15 | 14 | 9 | 0 | 13 |
| 11 | 4 | 3 | 7 | 8 | 1 | 2 | 6 | 5 | 10 | 15 | 12 | 13 | 0 | 9 | 14 |
| 12 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 15 | 14 | 13 | 0 | 11 | 10 | 9 |
| 13 | 5 | 6 | 2 | 1 | 8 | 7 | 3 | 4 | 14 | 9 | 0 | 11 | 12 | 15 | 10 |
| 14 | 6 | 5 | 1 | 2 | 7 | 8 | 4 | 3 | 13 | 0 | 9 | 10 | 15 | 12 | 11 |
| 15 | 7 | 8 | 5 | 6 | 3 | 4 | 1 | 2 | 12 | 13 | 14 | 9 | 10 | 11 | 0 |
Centre: 0 12
Centrum: 0 9 12 15
Nucleus: 0 12
Left Nucleus: 0 9 10 11 12 13 14 15
Middle Nucleus: 0 12
Right Nucleus: 0 12
1 Element of order 1: 0
5 Elements of order 2: 1 8 9 12 15
10 Elements of order 4: 2 3 4 5 6 7 10 11 13 14
Commutator Subloop: 0 12
Associator Subloop: 0 12
2 Conjugacy Classes of size 1:
7 Conjugacy Classes of size 2:
Automorphic Inverse Property: FAILS. (1-1)(3-1) neq (1*3)-1
Al Property: FAILS. The left inner mapping L1,1 = (2,7)(3,6)(4,5)(9,15)(10,14)(11,13) is not an automorphism. L1,1(2*3) neq L1,1(2)*L1,1(3)
Ar Property: HOLDS (i.e. every right inner mapping Ra,b is an automorphism)
Right (Left, Full) Mult Group Orders: 32 (1024, 2048)
/ revised October, 2001