| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 1 | 0 | 3 | 2 | 7 | 6 | 5 | 4 | 9 | 15 | 11 | 14 | 10 | 8 | 12 | 13 |
| 2 | 3 | 0 | 1 | 5 | 4 | 7 | 6 | 10 | 11 | 8 | 9 | 13 | 12 | 15 | 14 |
| 3 | 2 | 1 | 0 | 6 | 7 | 4 | 5 | 11 | 14 | 9 | 15 | 8 | 10 | 13 | 12 |
| 4 | 7 | 5 | 6 | 0 | 2 | 3 | 1 | 15 | 13 | 14 | 12 | 11 | 9 | 10 | 8 |
| 5 | 6 | 4 | 7 | 2 | 0 | 1 | 3 | 14 | 12 | 15 | 13 | 9 | 11 | 8 | 10 |
| 6 | 5 | 7 | 4 | 3 | 1 | 0 | 2 | 12 | 10 | 13 | 8 | 15 | 14 | 9 | 11 |
| 7 | 4 | 6 | 5 | 1 | 3 | 2 | 0 | 13 | 8 | 12 | 10 | 14 | 15 | 11 | 9 |
| 8 | 12 | 10 | 13 | 15 | 14 | 11 | 9 | 4 | 6 | 5 | 7 | 1 | 3 | 2 | 0 |
| 9 | 14 | 11 | 15 | 13 | 12 | 10 | 8 | 7 | 2 | 6 | 0 | 4 | 5 | 3 | 1 |
| 10 | 13 | 8 | 12 | 14 | 15 | 9 | 11 | 5 | 7 | 4 | 6 | 3 | 1 | 0 | 2 |
| 11 | 15 | 9 | 14 | 12 | 13 | 8 | 10 | 6 | 0 | 7 | 2 | 5 | 4 | 1 | 3 |
| 12 | 8 | 13 | 10 | 11 | 9 | 15 | 14 | 3 | 4 | 1 | 5 | 2 | 0 | 7 | 6 |
| 13 | 10 | 12 | 8 | 9 | 11 | 14 | 15 | 1 | 5 | 3 | 4 | 0 | 2 | 6 | 7 |
| 14 | 9 | 15 | 11 | 10 | 8 | 13 | 12 | 2 | 1 | 0 | 3 | 6 | 7 | 4 | 5 |
| 15 | 11 | 14 | 9 | 8 | 10 | 12 | 13 | 0 | 3 | 2 | 1 | 7 | 6 | 5 | 4 |
Centre: 0 2
Centrum: 0 2 4 5
Nucleus: 0 2
Left Nucleus: 0 2 4 5
Middle Nucleus: 0 2
Right Nucleus: 0 2
1 Element of order 1: 0
7 Elements of order 2: 1 2 3 4 5 6 7
8 Elements of order 4: 8 9 10 11 12 13 14 15
Commutator Subloop: 0 2 4 5
Associator Subloop: 0 2 4 5
2 Conjugacy Classes of size 1:
1 Conjugacy Class of size 2:
3 Conjugacy Classes of size 4:
Automorphic Inverse Property: FAILS. (1-1)(9-1) neq (1*9)-1
Al Property: FAILS. The left inner mapping L1,8 = (4,5)(6,7)(8,15)(9,13)(10,14)(11,12) is not an automorphism. L1,8(4*8) neq L1,8(4)*L1,8(8)
Ar Property: FAILS. The right inner mapping R1,8 = (1,7)(3,6)(8,15)(10,14) is not an automorphism. R1,8(8*1) neq R1,8(8)*R1,8(1)
Right (Left, Full) Mult Group Orders: 64 (4096, 16384)
/ revised October, 2001