| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| 1 | 0 | 3 | 2 | 5 | 4 | 7 | 6 | 9 | 8 | 11 | 10 | 13 | 12 | 15 | 14 | 17 | 16 | 19 | 18 | 21 | 20 | 23 | 22 | 25 | 24 | 27 | 26 |
| 2 | 3 | 26 | 27 | 1 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 25 | 24 |
| 3 | 2 | 27 | 26 | 0 | 1 | 5 | 4 | 7 | 6 | 9 | 8 | 11 | 10 | 13 | 12 | 15 | 14 | 17 | 16 | 19 | 18 | 21 | 20 | 23 | 22 | 24 | 25 |
| 4 | 5 | 1 | 0 | 7 | 6 | 9 | 8 | 11 | 10 | 13 | 12 | 15 | 14 | 17 | 16 | 19 | 18 | 21 | 20 | 23 | 22 | 25 | 24 | 26 | 27 | 3 | 2 |
| 5 | 4 | 0 | 1 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 27 | 26 | 2 | 3 |
| 6 | 7 | 4 | 5 | 9 | 8 | 11 | 10 | 13 | 12 | 15 | 14 | 17 | 16 | 19 | 18 | 21 | 20 | 23 | 22 | 25 | 24 | 26 | 27 | 2 | 3 | 1 | 0 |
| 7 | 6 | 5 | 4 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 27 | 26 | 3 | 2 | 0 | 1 |
| 8 | 9 | 6 | 7 | 11 | 10 | 13 | 12 | 15 | 14 | 17 | 16 | 19 | 18 | 21 | 20 | 23 | 22 | 25 | 24 | 26 | 27 | 2 | 3 | 0 | 1 | 4 | 5 |
| 9 | 8 | 7 | 6 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 27 | 26 | 3 | 2 | 1 | 0 | 5 | 4 |
| 10 | 11 | 8 | 9 | 13 | 12 | 15 | 14 | 17 | 16 | 19 | 18 | 21 | 20 | 23 | 22 | 25 | 24 | 26 | 27 | 2 | 3 | 0 | 1 | 5 | 4 | 6 | 7 |
| 11 | 10 | 9 | 8 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 27 | 26 | 3 | 2 | 1 | 0 | 4 | 5 | 7 | 6 |
| 12 | 13 | 10 | 11 | 15 | 14 | 17 | 16 | 19 | 18 | 21 | 20 | 23 | 22 | 25 | 24 | 26 | 27 | 2 | 3 | 0 | 1 | 5 | 4 | 7 | 6 | 8 | 9 |
| 13 | 12 | 11 | 10 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 27 | 26 | 3 | 2 | 1 | 0 | 4 | 5 | 6 | 7 | 9 | 8 |
| 14 | 15 | 12 | 13 | 17 | 16 | 19 | 18 | 21 | 20 | 23 | 22 | 25 | 24 | 26 | 27 | 2 | 3 | 0 | 1 | 5 | 4 | 7 | 6 | 9 | 8 | 10 | 11 |
| 15 | 14 | 13 | 12 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 27 | 26 | 3 | 2 | 1 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 11 | 10 |
| 16 | 17 | 14 | 15 | 19 | 18 | 21 | 20 | 23 | 22 | 25 | 24 | 26 | 27 | 2 | 3 | 0 | 1 | 5 | 4 | 7 | 6 | 9 | 8 | 11 | 10 | 12 | 13 |
| 17 | 16 | 15 | 14 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 27 | 26 | 3 | 2 | 1 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 13 | 12 |
| 18 | 19 | 16 | 17 | 21 | 20 | 23 | 22 | 25 | 24 | 26 | 27 | 2 | 3 | 0 | 1 | 5 | 4 | 7 | 6 | 9 | 8 | 11 | 10 | 13 | 12 | 14 | 15 |
| 19 | 18 | 17 | 16 | 20 | 21 | 22 | 23 | 24 | 25 | 27 | 26 | 3 | 2 | 1 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 15 | 14 |
| 20 | 21 | 18 | 19 | 23 | 22 | 25 | 24 | 26 | 27 | 2 | 3 | 0 | 1 | 5 | 4 | 7 | 6 | 9 | 8 | 11 | 10 | 13 | 12 | 15 | 14 | 16 | 17 |
| 21 | 20 | 19 | 18 | 22 | 23 | 24 | 25 | 27 | 26 | 3 | 2 | 1 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 17 | 16 |
| 22 | 23 | 20 | 21 | 25 | 24 | 26 | 27 | 2 | 3 | 0 | 1 | 5 | 4 | 7 | 6 | 9 | 8 | 11 | 10 | 13 | 12 | 15 | 14 | 17 | 16 | 18 | 19 |
| 23 | 22 | 21 | 20 | 24 | 25 | 27 | 26 | 3 | 2 | 1 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 19 | 18 |
| 24 | 25 | 22 | 23 | 26 | 27 | 2 | 3 | 0 | 1 | 5 | 4 | 7 | 6 | 9 | 8 | 11 | 10 | 13 | 12 | 15 | 14 | 17 | 16 | 19 | 18 | 20 | 21 |
| 25 | 24 | 23 | 22 | 27 | 26 | 3 | 2 | 1 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 21 | 20 |
| 26 | 27 | 25 | 24 | 3 | 2 | 1 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 23 | 22 |
| 27 | 26 | 24 | 25 | 2 | 3 | 0 | 1 | 5 | 4 | 7 | 6 | 9 | 8 | 11 | 10 | 13 | 12 | 15 | 14 | 17 | 16 | 19 | 18 | 21 | 20 | 22 | 23 |
Centre: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Centrum: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Left Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Middle Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Right Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 Element of order 1: 0
3 Elements of order 2: 1 16 17
6 Elements of order 7: 7 11 15 19 23 26
18 Elements of order 14: 2 3 4 5 6 8 9 10 12 13 14 18 20 21 22 24 25 27
Commutator Subloop: 0
Associator Subloop: 0
28 Conjugacy Classes of size 1:
Automorphic Inverse Property: HOLDS
Al Property: HOLDS (i.e. every left inner mapping La,b is an automorphism)
Ar Property: HOLDS (i.e. every right inner mapping Ra,b is an automorphism)
Right (Left, Full) Mult Group Orders: 28 (28, 28)
/ revised November, 2001