| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 1 | 7 | 0 | 11 | 10 | 8 | 9 | 2 | 6 | 5 | 3 | 4 |
| 2 | 0 | 7 | 10 | 11 | 9 | 8 | 1 | 5 | 6 | 4 | 3 |
| 3 | 9 | 8 | 7 | 0 | 11 | 10 | 4 | 1 | 2 | 5 | 6 |
| 4 | 8 | 9 | 0 | 7 | 10 | 11 | 3 | 2 | 1 | 6 | 5 |
| 5 | 10 | 11 | 9 | 8 | 7 | 0 | 6 | 3 | 4 | 2 | 1 |
| 6 | 11 | 10 | 8 | 9 | 0 | 7 | 5 | 4 | 3 | 1 | 2 |
| 7 | 2 | 1 | 4 | 3 | 6 | 5 | 0 | 9 | 8 | 11 | 10 |
| 8 | 3 | 4 | 5 | 6 | 2 | 1 | 9 | 11 | 10 | 0 | 7 |
| 9 | 4 | 3 | 6 | 5 | 1 | 2 | 8 | 10 | 11 | 7 | 0 |
| 10 | 6 | 5 | 1 | 2 | 3 | 4 | 11 | 0 | 7 | 9 | 8 |
| 11 | 5 | 6 | 2 | 1 | 4 | 3 | 10 | 7 | 0 | 8 | 9 |
Centre: 0 7
Centrum: 0 7
Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11
Left Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11
Middle Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11
Right Nucleus: 0 1 2 3 4 5 6 7 8 9 10 11
1 Element of order 1: 0
1 Element of order 2: 7
2 Elements of order 3: 9 11
6 Elements of order 4: 1 2 3 4 5 6
2 Elements of order 6: 8 10
Commutator Subloop: 0 9 11
Associator Subloop: 0
2 Conjugacy Classes of size 1:
2 Conjugacy Classes of size 2:
2 Conjugacy Classes of size 3:
Automorphic Inverse Property: FAILS. (1-1)(4-1) neq (1*4)-1
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: 12 (12, 72)
/ revised November, 2001