0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
1 | 0 | 3 | 2 | 7 | 6 | 5 | 4 | 9 | 15 | 14 | 10 | 8 | 11 | 13 | 12 |
2 | 3 | 0 | 1 | 6 | 7 | 4 | 5 | 10 | 11 | 15 | 12 | 14 | 8 | 9 | 13 |
3 | 2 | 1 | 0 | 5 | 4 | 7 | 6 | 11 | 13 | 9 | 15 | 10 | 12 | 8 | 14 |
4 | 7 | 6 | 5 | 0 | 3 | 2 | 1 | 15 | 12 | 13 | 14 | 9 | 10 | 11 | 8 |
5 | 6 | 7 | 4 | 3 | 0 | 1 | 2 | 14 | 10 | 12 | 8 | 13 | 9 | 15 | 11 |
6 | 5 | 4 | 7 | 2 | 1 | 0 | 3 | 13 | 14 | 8 | 9 | 11 | 15 | 12 | 10 |
7 | 4 | 5 | 6 | 1 | 2 | 3 | 0 | 12 | 8 | 11 | 13 | 15 | 14 | 10 | 9 |
8 | 12 | 13 | 11 | 15 | 14 | 10 | 9 | 4 | 1 | 6 | 5 | 7 | 2 | 3 | 0 |
9 | 15 | 14 | 10 | 12 | 13 | 11 | 8 | 7 | 4 | 3 | 6 | 0 | 5 | 2 | 1 |
10 | 14 | 15 | 9 | 13 | 12 | 8 | 11 | 6 | 3 | 0 | 1 | 5 | 4 | 7 | 2 |
11 | 13 | 12 | 8 | 14 | 15 | 9 | 10 | 5 | 6 | 7 | 0 | 2 | 1 | 4 | 3 |
12 | 8 | 11 | 13 | 9 | 10 | 14 | 15 | 1 | 0 | 5 | 2 | 4 | 3 | 6 | 7 |
13 | 11 | 8 | 12 | 10 | 9 | 15 | 14 | 2 | 5 | 4 | 7 | 3 | 0 | 1 | 6 |
14 | 10 | 9 | 15 | 11 | 8 | 12 | 13 | 3 | 2 | 1 | 4 | 6 | 7 | 0 | 5 |
15 | 9 | 10 | 14 | 8 | 11 | 13 | 12 | 0 | 7 | 2 | 3 | 1 | 6 | 5 | 4 |
Centre: 0 4
Centrum: 0 4
Nucleus: 0 4
Left Nucleus: 0 4
Middle Nucleus: 0 4
Right Nucleus: 0 4
1 Element of order 1: 0
11 Elements of order 2: 1 2 3 4 5 6 7 10 11 13 14
4 Elements of order 4: 8 9 12 15
Commutator Subloop: 0 4
Associator Subloop: 0 4
2 Conjugacy Classes of size 1:
7 Conjugacy Classes of size 2:
Automorphic Inverse Property: FAILS. (2-1)(9-1) neq (2*9)-1
Al Property: FAILS. The left inner mapping L1,8 = (10,13)(11,14) is not an automorphism. L1,8(2*8) neq L1,8(2)*L1,8(8)
Ar Property: HOLDS (i.e. every right inner mapping Ra,b is an automorphism)
Right (Left, Full) Mult Group Orders: 128 (1024, 2048)