| 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 | 24 | 16 | 26 | 15 | 23 | 20 | 19 | 27 | 17 | 22 | 21 | 18 | 0 | 25 | 8 | 10 | 6 | 3 | 12 | 14 | 4 | 5 | 13 | 11 | 2 | 9 | 7 |
| 2 | 16 | 26 | 15 | 23 | 20 | 19 | 24 | 0 | 27 | 17 | 22 | 21 | 25 | 18 | 13 | 9 | 7 | 4 | 11 | 12 | 5 | 6 | 14 | 10 | 3 | 8 | 1 |
| 3 | 26 | 15 | 23 | 20 | 19 | 24 | 16 | 25 | 0 | 27 | 17 | 22 | 18 | 21 | 14 | 8 | 1 | 5 | 10 | 11 | 6 | 7 | 12 | 9 | 4 | 13 | 2 |
| 4 | 15 | 23 | 20 | 19 | 24 | 16 | 26 | 18 | 25 | 0 | 27 | 17 | 21 | 22 | 12 | 13 | 2 | 6 | 9 | 10 | 7 | 1 | 11 | 8 | 5 | 14 | 3 |
| 5 | 23 | 20 | 19 | 24 | 16 | 26 | 15 | 21 | 18 | 25 | 0 | 27 | 22 | 17 | 11 | 14 | 3 | 7 | 8 | 9 | 1 | 2 | 10 | 13 | 6 | 12 | 4 |
| 6 | 20 | 19 | 24 | 16 | 26 | 15 | 23 | 22 | 21 | 18 | 25 | 0 | 17 | 27 | 10 | 12 | 4 | 1 | 13 | 8 | 2 | 3 | 9 | 14 | 7 | 11 | 5 |
| 7 | 19 | 24 | 16 | 26 | 15 | 23 | 20 | 17 | 22 | 21 | 18 | 25 | 27 | 0 | 9 | 11 | 5 | 2 | 14 | 13 | 3 | 4 | 8 | 12 | 1 | 10 | 6 |
| 8 | 27 | 0 | 25 | 18 | 21 | 22 | 17 | 26 | 16 | 24 | 19 | 20 | 15 | 23 | 3 | 1 | 10 | 14 | 6 | 5 | 12 | 11 | 4 | 7 | 13 | 2 | 9 |
| 9 | 17 | 27 | 0 | 25 | 18 | 21 | 22 | 16 | 24 | 19 | 20 | 23 | 26 | 15 | 2 | 7 | 11 | 13 | 5 | 4 | 14 | 12 | 3 | 6 | 8 | 1 | 10 |
| 10 | 22 | 17 | 27 | 0 | 25 | 18 | 21 | 24 | 19 | 20 | 23 | 15 | 16 | 26 | 1 | 6 | 12 | 8 | 4 | 3 | 13 | 14 | 2 | 5 | 9 | 7 | 11 |
| 11 | 21 | 22 | 17 | 27 | 0 | 25 | 18 | 19 | 20 | 23 | 15 | 26 | 24 | 16 | 7 | 5 | 14 | 9 | 3 | 2 | 8 | 13 | 1 | 4 | 10 | 6 | 12 |
| 12 | 18 | 21 | 22 | 17 | 27 | 0 | 25 | 20 | 23 | 15 | 26 | 16 | 19 | 24 | 6 | 4 | 13 | 10 | 2 | 1 | 9 | 8 | 7 | 3 | 11 | 5 | 14 |
| 13 | 0 | 25 | 18 | 21 | 22 | 17 | 27 | 15 | 26 | 16 | 24 | 19 | 23 | 20 | 4 | 2 | 9 | 12 | 7 | 6 | 11 | 10 | 5 | 1 | 14 | 3 | 8 |
| 14 | 25 | 18 | 21 | 22 | 17 | 27 | 0 | 23 | 15 | 26 | 16 | 24 | 20 | 19 | 5 | 3 | 8 | 11 | 1 | 7 | 10 | 9 | 6 | 2 | 12 | 4 | 13 |
| 15 | 8 | 13 | 14 | 12 | 11 | 10 | 9 | 3 | 2 | 1 | 7 | 6 | 4 | 5 | 18 | 0 | 16 | 20 | 17 | 22 | 19 | 24 | 21 | 27 | 23 | 25 | 26 |
| 16 | 10 | 9 | 8 | 13 | 14 | 12 | 11 | 1 | 7 | 6 | 5 | 4 | 2 | 3 | 0 | 17 | 19 | 15 | 21 | 18 | 23 | 20 | 25 | 22 | 26 | 27 | 24 |
| 17 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 10 | 11 | 12 | 14 | 13 | 9 | 8 | 16 | 19 | 21 | 0 | 23 | 15 | 25 | 18 | 26 | 20 | 27 | 24 | 22 |
| 18 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 14 | 13 | 8 | 9 | 10 | 12 | 11 | 20 | 15 | 0 | 22 | 16 | 24 | 17 | 27 | 19 | 26 | 21 | 23 | 25 |
| 19 | 12 | 11 | 10 | 9 | 8 | 13 | 14 | 6 | 5 | 4 | 3 | 2 | 7 | 1 | 17 | 21 | 23 | 16 | 25 | 0 | 26 | 15 | 27 | 18 | 24 | 22 | 20 |
| 20 | 14 | 12 | 11 | 10 | 9 | 8 | 13 | 5 | 4 | 3 | 2 | 1 | 6 | 7 | 22 | 18 | 15 | 24 | 0 | 27 | 16 | 26 | 17 | 25 | 19 | 21 | 23 |
| 21 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 12 | 14 | 13 | 8 | 9 | 11 | 10 | 19 | 23 | 25 | 17 | 26 | 16 | 27 | 0 | 24 | 15 | 22 | 20 | 18 |
| 22 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 11 | 12 | 14 | 13 | 8 | 10 | 9 | 24 | 20 | 18 | 27 | 15 | 26 | 0 | 25 | 16 | 23 | 17 | 19 | 21 |
| 23 | 13 | 14 | 12 | 11 | 10 | 9 | 8 | 4 | 3 | 2 | 1 | 7 | 5 | 6 | 21 | 25 | 26 | 19 | 27 | 17 | 24 | 16 | 22 | 0 | 20 | 18 | 15 |
| 24 | 11 | 10 | 9 | 8 | 13 | 14 | 12 | 7 | 6 | 5 | 4 | 3 | 1 | 2 | 27 | 22 | 20 | 26 | 18 | 25 | 15 | 23 | 0 | 21 | 16 | 17 | 19 |
| 25 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 13 | 8 | 9 | 10 | 11 | 14 | 12 | 23 | 26 | 27 | 21 | 24 | 19 | 22 | 17 | 20 | 16 | 18 | 15 | 0 |
| 26 | 9 | 8 | 13 | 14 | 12 | 11 | 10 | 2 | 1 | 7 | 6 | 5 | 3 | 4 | 25 | 27 | 24 | 23 | 22 | 21 | 20 | 19 | 18 | 17 | 15 | 0 | 16 |
| 27 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 9 | 10 | 11 | 12 | 14 | 8 | 13 | 26 | 24 | 22 | 25 | 20 | 23 | 18 | 21 | 15 | 19 | 0 | 16 | 17 |
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
1 Element of order 2: 26
2 Elements of order 4: 2 8
6 Elements of order 7: 17 18 21 22 25 27
6 Elements of order 14: 15 16 19 20 23 24
12 Elements of order 28: 1 3 4 5 6 7 9 10 11 12 13 14
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