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