| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 1 | 4 | 0 | 2 | 6 | 3 | 5 | 10 | 11 | 12 | 13 | 7 | 8 | 9 | 20 | 16 | 17 | 14 | 19 | 15 | 18 |
| 2 | 0 | 3 | 5 | 1 | 6 | 4 | 11 | 12 | 13 | 7 | 8 | 9 | 10 | 17 | 19 | 15 | 16 | 20 | 18 | 14 |
| 3 | 2 | 5 | 6 | 0 | 4 | 1 | 8 | 9 | 10 | 11 | 12 | 13 | 7 | 16 | 18 | 19 | 15 | 14 | 20 | 17 |
| 4 | 6 | 1 | 0 | 5 | 2 | 3 | 13 | 7 | 8 | 9 | 10 | 11 | 12 | 18 | 17 | 14 | 20 | 15 | 16 | 19 |
| 5 | 3 | 6 | 4 | 2 | 1 | 0 | 12 | 13 | 7 | 8 | 9 | 10 | 11 | 15 | 20 | 18 | 19 | 17 | 14 | 16 |
| 6 | 5 | 4 | 1 | 3 | 0 | 2 | 9 | 10 | 11 | 12 | 13 | 7 | 8 | 19 | 14 | 20 | 18 | 16 | 17 | 15 |
| 7 | 9 | 12 | 10 | 11 | 8 | 13 | 16 | 18 | 17 | 19 | 14 | 15 | 20 | 4 | 2 | 0 | 1 | 5 | 3 | 6 |
| 8 | 10 | 13 | 11 | 12 | 9 | 7 | 19 | 14 | 15 | 20 | 16 | 18 | 17 | 0 | 5 | 3 | 2 | 4 | 6 | 1 |
| 9 | 11 | 7 | 12 | 13 | 10 | 8 | 20 | 16 | 18 | 17 | 19 | 14 | 15 | 3 | 4 | 6 | 5 | 0 | 1 | 2 |
| 10 | 12 | 8 | 13 | 7 | 11 | 9 | 17 | 19 | 14 | 15 | 20 | 16 | 18 | 6 | 0 | 1 | 4 | 3 | 2 | 5 |
| 11 | 13 | 9 | 7 | 8 | 12 | 10 | 15 | 20 | 16 | 18 | 17 | 19 | 14 | 1 | 3 | 2 | 0 | 6 | 5 | 4 |
| 12 | 7 | 10 | 8 | 9 | 13 | 11 | 18 | 17 | 19 | 14 | 15 | 20 | 16 | 2 | 6 | 5 | 3 | 1 | 4 | 0 |
| 13 | 8 | 11 | 9 | 10 | 7 | 12 | 14 | 15 | 20 | 16 | 18 | 17 | 19 | 5 | 1 | 4 | 6 | 2 | 0 | 3 |
| 14 | 19 | 15 | 20 | 17 | 16 | 18 | 4 | 0 | 3 | 6 | 1 | 2 | 5 | 8 | 12 | 13 | 7 | 10 | 11 | 9 |
| 15 | 14 | 20 | 16 | 19 | 18 | 17 | 2 | 5 | 4 | 0 | 3 | 6 | 1 | 13 | 10 | 11 | 12 | 8 | 9 | 7 |
| 16 | 20 | 18 | 17 | 15 | 19 | 14 | 0 | 3 | 6 | 1 | 2 | 5 | 4 | 9 | 13 | 7 | 8 | 11 | 12 | 10 |
| 17 | 18 | 19 | 14 | 16 | 15 | 20 | 1 | 2 | 5 | 4 | 0 | 3 | 6 | 12 | 9 | 10 | 11 | 7 | 8 | 13 |
| 18 | 16 | 17 | 19 | 20 | 14 | 15 | 5 | 4 | 0 | 3 | 6 | 1 | 2 | 7 | 11 | 12 | 13 | 9 | 10 | 8 |
| 19 | 17 | 14 | 15 | 18 | 20 | 16 | 3 | 6 | 1 | 2 | 5 | 4 | 0 | 10 | 7 | 8 | 9 | 12 | 13 | 11 |
| 20 | 15 | 16 | 18 | 14 | 17 | 19 | 6 | 1 | 2 | 5 | 4 | 0 | 3 | 11 | 8 | 9 | 10 | 13 | 7 | 12 |
Centre: 0
Centrum: 0
Nucleus: 0
Left Nucleus: 0 1 2 3 4 5 6
Middle Nucleus: 0
Right Nucleus: 0
1 Element of order 1: 0
14 Elements of order 3: 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6 Elements of order 7: 1 2 3 4 5 6
Commutator Subloop: 0 1 2 3 4 5 6
Associator Subloop: 0 1 2 3 4 5 6
1 Conjugacy Class of size 1:
1 Conjugacy Class of size 6:
2 Conjugacy Classes of size 7:
Automorphic Inverse Property: HOLDS
Al Property: FAILS. The left inner mapping L1,7 = (7,11,8,12,9,13,10)(14,16,19,20,17,15,18) is not an automorphism. L1,7(7*7) neq L1,7(7)*L1,7(7)
Ar Property: HOLDS (i.e. every right inner mapping Ra,b is an automorphism)
Right (Left, Full) Mult Group Orders: 147 (12348, 37044)
/ revised November, 2001