| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 1 | 0 | 3 | 5 | 2 | 4 | 8 | 6 | 15 | 12 | 13 | 14 | 9 | 10 | 11 | 7 |
| 2 | 3 | 0 | 1 | 6 | 7 | 4 | 5 | 9 | 8 | 11 | 10 | 15 | 14 | 13 | 12 |
| 3 | 2 | 1 | 7 | 0 | 6 | 9 | 4 | 12 | 15 | 14 | 13 | 8 | 11 | 10 | 5 |
| 4 | 5 | 6 | 0 | 7 | 1 | 11 | 3 | 14 | 13 | 12 | 15 | 10 | 9 | 8 | 2 |
| 5 | 4 | 7 | 6 | 1 | 0 | 3 | 2 | 11 | 10 | 9 | 8 | 13 | 12 | 15 | 14 |
| 6 | 7 | 4 | 2 | 5 | 3 | 10 | 1 | 13 | 14 | 15 | 12 | 11 | 8 | 9 | 0 |
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 | 10 | 11 | 8 | 9 | 14 | 15 | 12 | 13 |
| 8 | 15 | 9 | 12 | 14 | 11 | 13 | 10 | 0 | 2 | 7 | 5 | 3 | 6 | 4 | 1 |
| 9 | 12 | 8 | 15 | 13 | 10 | 14 | 11 | 2 | 0 | 5 | 7 | 1 | 4 | 6 | 3 |
| 10 | 13 | 11 | 14 | 12 | 9 | 15 | 8 | 7 | 5 | 0 | 2 | 4 | 1 | 3 | 6 |
| 11 | 14 | 10 | 13 | 15 | 8 | 12 | 9 | 5 | 7 | 2 | 0 | 6 | 3 | 1 | 4 |
| 12 | 9 | 15 | 10 | 8 | 13 | 2 | 14 | 3 | 1 | 4 | 6 | 0 | 5 | 7 | 11 |
| 13 | 10 | 14 | 9 | 11 | 12 | 7 | 15 | 6 | 4 | 1 | 3 | 5 | 0 | 2 | 8 |
| 14 | 11 | 13 | 8 | 10 | 15 | 5 | 12 | 4 | 6 | 3 | 1 | 7 | 2 | 0 | 9 |
| 15 | 8 | 12 | 11 | 9 | 14 | 0 | 13 | 1 | 3 | 6 | 4 | 2 | 7 | 5 | 10 |
Centre: 0
Centrum: 0 2 5 7 8 9 10 11
Nucleus: 0
Left Nucleus: 0 2 5 7 8 9 10 11
Middle Nucleus: 0
Right Nucleus: 0
1 Element of order 1: 0
11 Elements of order 2: 1 2 5 7 8 9 10 11 12 13 14
4 Elements of order 4: 3 4 6 15
Commutator Subloop: 0 7 8 10
Associator Subloop: 0 7 8 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 = (2,5)(3,4)(6,15)(7,8) is not an automorphism. L1,1(2*4) neq L1,1(2)*L1,1(4)
Ar Property: FAILS. The right inner mapping R1,2 = (1,6)(3,4)(12,14)(13,15) is not an automorphism. R1,2(1*1) neq R1,2(1)*R1,2(1)
Right (Left, Full) Mult Group Orders: 64 (18432, 36864)
/ revised November, 2001