| 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 |
| 1 | 2 | 0 | 4 | 5 | 3 | 10 | 8 | 9 | 7 | 11 | 6 | 13 | 14 | 12 | 17 | 15 | 16 | 20 | 18 | 19 | 22 | 23 | 21 | 26 | 24 | 25 |
| 2 | 0 | 1 | 5 | 3 | 4 | 11 | 9 | 7 | 8 | 6 | 10 | 14 | 12 | 13 | 16 | 17 | 15 | 19 | 20 | 18 | 23 | 21 | 22 | 25 | 26 | 24 |
| 3 | 4 | 5 | 6 | 10 | 11 | 17 | 1 | 2 | 0 | 16 | 15 | 8 | 9 | 7 | 18 | 19 | 20 | 26 | 24 | 25 | 13 | 14 | 12 | 23 | 22 | 21 |
| 4 | 5 | 3 | 10 | 11 | 6 | 16 | 2 | 0 | 1 | 15 | 17 | 9 | 7 | 8 | 20 | 18 | 19 | 25 | 26 | 24 | 14 | 12 | 13 | 21 | 23 | 22 |
| 5 | 3 | 4 | 11 | 6 | 10 | 15 | 0 | 1 | 2 | 17 | 16 | 7 | 8 | 9 | 19 | 20 | 18 | 24 | 25 | 26 | 12 | 13 | 14 | 22 | 21 | 23 |
| 6 | 10 | 11 | 17 | 16 | 15 | 20 | 4 | 5 | 3 | 19 | 18 | 2 | 0 | 1 | 26 | 24 | 25 | 21 | 23 | 22 | 9 | 7 | 8 | 12 | 14 | 13 |
| 7 | 8 | 9 | 1 | 2 | 0 | 4 | 12 | 13 | 14 | 5 | 3 | 21 | 22 | 23 | 6 | 11 | 10 | 17 | 15 | 16 | 25 | 24 | 26 | 18 | 19 | 20 |
| 8 | 9 | 7 | 2 | 0 | 1 | 5 | 13 | 14 | 12 | 3 | 4 | 22 | 23 | 21 | 10 | 6 | 11 | 16 | 17 | 15 | 24 | 26 | 25 | 20 | 18 | 19 |
| 9 | 7 | 8 | 0 | 1 | 2 | 3 | 14 | 12 | 13 | 4 | 5 | 23 | 21 | 22 | 11 | 10 | 6 | 15 | 16 | 17 | 26 | 25 | 24 | 19 | 20 | 18 |
| 10 | 11 | 6 | 16 | 15 | 17 | 19 | 5 | 3 | 4 | 18 | 20 | 0 | 1 | 2 | 25 | 26 | 24 | 22 | 21 | 23 | 7 | 8 | 9 | 13 | 12 | 14 |
| 11 | 6 | 10 | 15 | 17 | 16 | 18 | 3 | 4 | 5 | 20 | 19 | 1 | 2 | 0 | 24 | 25 | 26 | 23 | 22 | 21 | 8 | 9 | 7 | 14 | 13 | 12 |
| 12 | 13 | 14 | 8 | 9 | 7 | 2 | 21 | 22 | 23 | 0 | 1 | 25 | 24 | 26 | 4 | 3 | 5 | 10 | 6 | 11 | 19 | 18 | 20 | 17 | 15 | 16 |
| 13 | 14 | 12 | 9 | 7 | 8 | 0 | 22 | 23 | 21 | 1 | 2 | 24 | 26 | 25 | 5 | 4 | 3 | 11 | 10 | 6 | 18 | 20 | 19 | 16 | 17 | 15 |
| 14 | 12 | 13 | 7 | 8 | 9 | 1 | 23 | 21 | 22 | 2 | 0 | 26 | 25 | 24 | 3 | 5 | 4 | 6 | 11 | 10 | 20 | 19 | 18 | 15 | 16 | 17 |
| 15 | 17 | 16 | 18 | 20 | 19 | 26 | 6 | 10 | 11 | 25 | 24 | 4 | 5 | 3 | 23 | 22 | 21 | 12 | 14 | 13 | 2 | 0 | 1 | 7 | 9 | 8 |
| 16 | 15 | 17 | 19 | 18 | 20 | 24 | 11 | 6 | 10 | 26 | 25 | 3 | 4 | 5 | 22 | 21 | 23 | 14 | 13 | 12 | 1 | 2 | 0 | 9 | 8 | 7 |
| 17 | 16 | 15 | 20 | 19 | 18 | 25 | 10 | 11 | 6 | 24 | 26 | 5 | 3 | 4 | 21 | 23 | 22 | 13 | 12 | 14 | 0 | 1 | 2 | 8 | 7 | 9 |
| 18 | 20 | 19 | 26 | 25 | 24 | 21 | 17 | 16 | 15 | 22 | 23 | 10 | 11 | 6 | 12 | 14 | 13 | 8 | 7 | 9 | 5 | 3 | 4 | 1 | 0 | 2 |
| 19 | 18 | 20 | 24 | 26 | 25 | 23 | 15 | 17 | 16 | 21 | 22 | 6 | 10 | 11 | 14 | 13 | 12 | 7 | 9 | 8 | 4 | 5 | 3 | 0 | 2 | 1 |
| 20 | 19 | 18 | 25 | 24 | 26 | 22 | 16 | 15 | 17 | 23 | 21 | 11 | 6 | 10 | 13 | 12 | 14 | 9 | 8 | 7 | 3 | 4 | 5 | 2 | 1 | 0 |
| 21 | 22 | 23 | 13 | 14 | 12 | 9 | 25 | 24 | 26 | 7 | 8 | 19 | 18 | 20 | 2 | 1 | 0 | 5 | 4 | 3 | 15 | 17 | 16 | 10 | 6 | 11 |
| 22 | 23 | 21 | 14 | 12 | 13 | 7 | 24 | 26 | 25 | 8 | 9 | 18 | 20 | 19 | 0 | 2 | 1 | 3 | 5 | 4 | 17 | 16 | 15 | 11 | 10 | 6 |
| 23 | 21 | 22 | 12 | 13 | 14 | 8 | 26 | 25 | 24 | 9 | 7 | 20 | 19 | 18 | 1 | 0 | 2 | 4 | 3 | 5 | 16 | 15 | 17 | 6 | 11 | 10 |
| 24 | 26 | 25 | 23 | 21 | 22 | 12 | 18 | 20 | 19 | 13 | 14 | 17 | 16 | 15 | 7 | 9 | 8 | 1 | 0 | 2 | 10 | 11 | 6 | 3 | 5 | 4 |
| 25 | 24 | 26 | 22 | 23 | 21 | 14 | 19 | 18 | 20 | 12 | 13 | 15 | 17 | 16 | 9 | 8 | 7 | 0 | 2 | 1 | 6 | 10 | 11 | 5 | 4 | 3 |
| 26 | 25 | 24 | 21 | 22 | 23 | 13 | 20 | 19 | 18 | 14 | 12 | 16 | 15 | 17 | 8 | 7 | 9 | 2 | 1 | 0 | 11 | 6 | 10 | 4 | 3 | 5 |
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
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
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
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
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
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
1 Element of order 1: 0
2 Elements of order 3: 1 2
6 Elements of order 9: 15 16 17 21 22 23
18 Elements of order 27: 3 4 5 6 7 8 9 10 11 12 13 14 18 19 20 24 25 26
Commutator Subloop: 0
Associator Subloop: 0
27 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: 27 (27, 27)
/ revised October, 2001