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