| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 1 | 0 | 3 | 2 | 8 | 6 | 5 | 9 | 4 | 7 | 11 | 10 |
| 2 | 4 | 5 | 9 | 7 | 0 | 10 | 1 | 6 | 11 | 8 | 3 |
| 3 | 8 | 6 | 7 | 9 | 1 | 11 | 0 | 5 | 10 | 4 | 2 |
| 4 | 2 | 9 | 5 | 6 | 10 | 0 | 11 | 7 | 1 | 3 | 8 |
| 5 | 7 | 0 | 11 | 1 | 2 | 8 | 4 | 10 | 3 | 6 | 9 |
| 6 | 9 | 1 | 10 | 0 | 3 | 4 | 8 | 11 | 2 | 5 | 7 |
| 7 | 5 | 11 | 0 | 10 | 8 | 2 | 3 | 1 | 4 | 9 | 6 |
| 8 | 3 | 7 | 6 | 5 | 11 | 1 | 10 | 9 | 0 | 2 | 4 |
| 9 | 6 | 10 | 1 | 11 | 4 | 3 | 2 | 0 | 8 | 7 | 5 |
| 10 | 11 | 4 | 8 | 2 | 9 | 7 | 6 | 3 | 5 | 0 | 1 |
| 11 | 10 | 8 | 4 | 3 | 7 | 9 | 5 | 2 | 6 | 1 | 0 |
Centre: 0
Centrum: 0
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
3 Elements of order 2: 1 10 11
8 Elements of order 3: 2 3 4 5 6 7 8 9
Commutator Subloop: 0 1 10 11
Associator Subloop: 0
1 Conjugacy Class of size 1:
1 Conjugacy Class of size 3:
2 Conjugacy Classes of size 4:
Automorphic Inverse Property: FAILS. (1-1)(3-1) neq (1*3)-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, 144)
/ revised November, 2001