| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 1 | 0 | 3 | 2 | 8 | 7 | 5 | 11 | 4 | 12 | 14 | 6 | 10 | 15 | 9 | 13 |
| 2 | 3 | 4 | 1 | 6 | 8 | 0 | 10 | 5 | 7 | 15 | 12 | 11 | 14 | 13 | 9 |
| 3 | 2 | 8 | 0 | 5 | 9 | 1 | 14 | 6 | 11 | 13 | 4 | 15 | 10 | 7 | 12 |
| 4 | 8 | 6 | 5 | 0 | 3 | 2 | 15 | 1 | 10 | 9 | 13 | 14 | 11 | 12 | 7 |
| 5 | 6 | 1 | 4 | 3 | 10 | 8 | 12 | 2 | 13 | 11 | 0 | 7 | 9 | 15 | 14 |
| 6 | 5 | 0 | 8 | 2 | 1 | 4 | 9 | 3 | 15 | 7 | 14 | 13 | 12 | 11 | 10 |
| 7 | 11 | 10 | 12 | 15 | 14 | 9 | 4 | 13 | 2 | 6 | 1 | 3 | 8 | 5 | 0 |
| 8 | 4 | 5 | 6 | 1 | 15 | 3 | 13 | 0 | 14 | 12 | 2 | 9 | 7 | 10 | 11 |
| 9 | 12 | 7 | 11 | 10 | 13 | 15 | 2 | 14 | 0 | 4 | 3 | 1 | 5 | 8 | 6 |
| 10 | 14 | 15 | 13 | 9 | 11 | 7 | 6 | 12 | 4 | 0 | 5 | 8 | 3 | 1 | 2 |
| 11 | 7 | 14 | 9 | 13 | 0 | 12 | 8 | 15 | 3 | 5 | 10 | 6 | 4 | 2 | 1 |
| 12 | 9 | 11 | 7 | 14 | 2 | 13 | 3 | 10 | 1 | 8 | 15 | 4 | 6 | 0 | 5 |
| 13 | 15 | 12 | 10 | 11 | 4 | 14 | 1 | 7 | 5 | 3 | 9 | 2 | 0 | 6 | 8 |
| 14 | 10 | 13 | 15 | 12 | 6 | 11 | 5 | 9 | 8 | 1 | 7 | 0 | 2 | 4 | 3 |
| 15 | 13 | 9 | 14 | 7 | 12 | 10 | 0 | 11 | 6 | 2 | 8 | 5 | 1 | 3 | 4 |
Centre: 0
Centrum: 0 4 9 10
Nucleus: 0
Left Nucleus: 0 4 9 10
Middle Nucleus: 0
Right Nucleus: 0
1 Element of order 1: 0
7 Elements of order 2: 1 3 4 8 9 10 13
8 Elements of order 4: 2 5 6 7 11 12 14 15
Commutator Subloop: 0 4 9 10
Associator Subloop: 0 4 9 10
1 Conjugacy Class of size 1:
1 Conjugacy Class of size 3:
3 Conjugacy Classes of size 4:
Automorphic Inverse Property: FAILS. (1-1)(3-1) neq (1*3)-1
Al Property: FAILS. The left inner mapping L1,1 = (5,11)(6,7)(9,10)(12,14) is not an automorphism. L1,1(2*4) neq L1,1(2)*L1,1(4)
Ar Property: FAILS. The right inner mapping R1,2 = (2,6)(3,5)(7,15)(11,13) is not an automorphism. R1,2(1*3) neq R1,2(1)*R1,2(3)
Right (Left, Full) Mult Group Orders: 128 (18432, 36864)
/ revised November, 2001