| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 1 | 11 | 13 | 12 | 0 | 9 | 10 | 14 | 15 | 2 | 3 | 4 | 6 | 5 | 7 | 8 |
| 2 | 10 | 12 | 13 | 9 | 0 | 11 | 15 | 14 | 1 | 4 | 3 | 5 | 6 | 8 | 7 |
| 3 | 9 | 14 | 15 | 10 | 11 | 0 | 13 | 12 | 4 | 1 | 2 | 8 | 7 | 5 | 6 |
| 4 | 0 | 15 | 14 | 11 | 10 | 9 | 12 | 13 | 3 | 2 | 1 | 7 | 8 | 6 | 5 |
| 5 | 15 | 0 | 9 | 13 | 12 | 14 | 10 | 11 | 6 | 7 | 8 | 2 | 1 | 3 | 4 |
| 6 | 14 | 9 | 0 | 12 | 13 | 15 | 11 | 10 | 5 | 8 | 7 | 1 | 2 | 4 | 3 |
| 7 | 12 | 10 | 11 | 14 | 15 | 13 | 0 | 9 | 8 | 5 | 6 | 4 | 3 | 1 | 2 |
| 8 | 13 | 11 | 10 | 15 | 14 | 12 | 9 | 0 | 7 | 6 | 5 | 3 | 4 | 2 | 1 |
| 9 | 2 | 1 | 4 | 3 | 6 | 5 | 8 | 7 | 0 | 11 | 10 | 13 | 12 | 15 | 14 |
| 10 | 3 | 4 | 1 | 2 | 7 | 8 | 5 | 6 | 11 | 0 | 9 | 15 | 14 | 13 | 12 |
| 11 | 4 | 3 | 2 | 1 | 8 | 7 | 6 | 5 | 10 | 9 | 0 | 14 | 15 | 12 | 13 |
| 12 | 6 | 5 | 8 | 7 | 2 | 1 | 4 | 3 | 13 | 15 | 14 | 0 | 9 | 11 | 10 |
| 13 | 5 | 6 | 7 | 8 | 1 | 2 | 3 | 4 | 12 | 14 | 15 | 9 | 0 | 10 | 11 |
| 14 | 7 | 8 | 5 | 6 | 3 | 4 | 1 | 2 | 15 | 13 | 12 | 11 | 10 | 0 | 9 |
| 15 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 14 | 12 | 13 | 10 | 11 | 9 | 0 |
Centre: 0
Centrum: 0 9 10 11 12 13 14 15
Nucleus: 0
Left Nucleus: 0 9 10 11 12 13 14 15
Middle Nucleus: 0
Right Nucleus: 0
1 Element of order 1: 0
9 Elements of order 2: 7 8 9 10 11 12 13 14 15
6 Elements of order 4: 1 2 3 4 5 6
Commutator Subloop: 0 9 10 11 12 13 14 15
Associator Subloop: 0 9 10 11 12 13 14 15
1 Conjugacy Class of size 1:
1 Conjugacy Class of size 7:
1 Conjugacy Class of size 8:
Automorphic Inverse Property: FAILS. (1-1)(3-1) neq (1*3)-1
Al Property: FAILS. The left inner mapping L1,1 = (2,8,5,3,7,6)(9,15,13,10,14,12) is not an automorphism. L1,1(1*2) neq L1,1(1)*L1,1(2)
Ar Property: FAILS. The right inner mapping R1,2 = (1,7)(2,8)(3,5)(4,6) is not an automorphism. R1,2(1*1) neq R1,2(1)*R1,2(1)
Right (Left, Full) Mult Group Orders: 128 (1625702400, 3251404800)
/ revised November, 2001