0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
1 | 2 | 5 | 0 | 3 | 6 | 7 | 4 | 9 | 15 | 13 | 14 | 8 | 10 | 11 | 12 |
2 | 5 | 6 | 1 | 0 | 7 | 4 | 3 | 14 | 11 | 9 | 12 | 10 | 8 | 15 | 13 |
3 | 0 | 1 | 4 | 7 | 2 | 5 | 6 | 11 | 13 | 8 | 15 | 14 | 9 | 12 | 10 |
4 | 3 | 0 | 7 | 6 | 1 | 2 | 5 | 13 | 10 | 12 | 9 | 11 | 15 | 8 | 14 |
5 | 6 | 7 | 2 | 1 | 4 | 3 | 0 | 10 | 14 | 15 | 8 | 13 | 12 | 9 | 11 |
6 | 7 | 4 | 5 | 2 | 3 | 0 | 1 | 15 | 12 | 11 | 10 | 9 | 14 | 13 | 8 |
7 | 4 | 3 | 6 | 5 | 0 | 1 | 2 | 12 | 8 | 14 | 13 | 15 | 11 | 10 | 9 |
8 | 10 | 13 | 12 | 14 | 9 | 15 | 11 | 6 | 1 | 3 | 5 | 7 | 2 | 4 | 0 |
9 | 15 | 11 | 13 | 10 | 14 | 12 | 8 | 7 | 6 | 2 | 4 | 0 | 3 | 5 | 1 |
10 | 13 | 9 | 8 | 12 | 15 | 11 | 14 | 3 | 2 | 0 | 6 | 4 | 1 | 7 | 5 |
11 | 14 | 12 | 15 | 9 | 8 | 10 | 13 | 5 | 4 | 6 | 0 | 2 | 7 | 1 | 3 |
12 | 8 | 10 | 14 | 11 | 13 | 9 | 15 | 1 | 0 | 4 | 2 | 6 | 5 | 3 | 7 |
13 | 9 | 15 | 10 | 8 | 11 | 14 | 12 | 2 | 5 | 1 | 7 | 3 | 0 | 6 | 4 |
14 | 12 | 8 | 11 | 15 | 10 | 13 | 9 | 4 | 3 | 7 | 1 | 5 | 6 | 0 | 2 |
15 | 11 | 14 | 9 | 13 | 12 | 8 | 10 | 0 | 7 | 5 | 3 | 1 | 4 | 2 | 6 |
Centre: 0 6
Centrum: 0 6 10 11
Nucleus: 0 6
Left Nucleus: 0 6 10 11
Middle Nucleus: 0 6
Right Nucleus: 0 6
1 Element of order 1: 0
5 Elements of order 2: 6 10 11 13 14
6 Elements of order 4: 2 4 8 9 12 15
4 Elements of order 8: 1 3 5 7
Commutator Subloop: 0 2 4 6
Associator Subloop: 0 2 4 6
2 Conjugacy Classes of size 1:
1 Conjugacy Class of size 2:
3 Conjugacy Classes of size 4:
Automorphic Inverse Property: FAILS. (1-1)(9-1) neq (1*9)-1
Al Property: FAILS. The left inner mapping L1,1 = (8,14)(9,11)(10,12)(13,15) is not an automorphism. L1,1(1*9) neq L1,1(1)*L1,1(9)
Ar Property: FAILS. The right inner mapping R1,8 = (1,5)(2,4)(3,7)(8,14)(9,12)(13,15) is not an automorphism. R1,8(1*8) neq R1,8(1)*R1,8(8)
Right (Left, Full) Mult Group Orders: 64 (1024, 4096)