| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
| 1 | 13 | 14 | 0 | 15 | 21 | 22 | 16 | 23 | 19 | 17 | 20 | 18 | 2 | 4 | 3 | 10 | 9 | 7 | 12 | 6 | 8 | 5 | 11 |
| 2 | 14 | 15 | 13 | 0 | 23 | 21 | 17 | 20 | 18 | 19 | 22 | 16 | 4 | 3 | 1 | 9 | 12 | 10 | 7 | 5 | 11 | 8 | 6 |
| 3 | 0 | 13 | 15 | 14 | 22 | 20 | 18 | 21 | 17 | 16 | 23 | 19 | 1 | 2 | 4 | 7 | 10 | 12 | 9 | 11 | 5 | 6 | 8 |
| 4 | 15 | 0 | 14 | 13 | 20 | 23 | 19 | 22 | 16 | 18 | 21 | 17 | 3 | 1 | 2 | 12 | 7 | 9 | 10 | 8 | 6 | 11 | 5 |
| 5 | 17 | 19 | 16 | 18 | 15 | 14 | 20 | 0 | 21 | 22 | 13 | 23 | 8 | 11 | 6 | 4 | 3 | 2 | 1 | 12 | 10 | 7 | 9 |
| 6 | 16 | 17 | 18 | 19 | 14 | 13 | 23 | 15 | 22 | 20 | 0 | 21 | 5 | 8 | 11 | 2 | 4 | 1 | 3 | 9 | 7 | 12 | 10 |
| 7 | 22 | 21 | 20 | 23 | 18 | 19 | 13 | 16 | 15 | 14 | 17 | 0 | 10 | 9 | 12 | 11 | 6 | 8 | 5 | 1 | 4 | 2 | 3 |
| 8 | 19 | 18 | 17 | 16 | 0 | 15 | 22 | 13 | 23 | 21 | 14 | 20 | 11 | 6 | 5 | 3 | 1 | 4 | 2 | 7 | 9 | 10 | 12 |
| 9 | 23 | 20 | 21 | 22 | 17 | 16 | 15 | 19 | 13 | 0 | 18 | 14 | 12 | 7 | 10 | 5 | 8 | 6 | 11 | 4 | 1 | 3 | 2 |
| 10 | 21 | 23 | 22 | 20 | 16 | 18 | 14 | 17 | 0 | 15 | 19 | 13 | 9 | 12 | 7 | 6 | 5 | 11 | 8 | 2 | 3 | 4 | 1 |
| 11 | 18 | 16 | 19 | 17 | 13 | 0 | 21 | 14 | 20 | 23 | 15 | 22 | 6 | 5 | 8 | 1 | 2 | 3 | 4 | 10 | 12 | 9 | 7 |
| 12 | 20 | 22 | 23 | 21 | 19 | 17 | 0 | 18 | 14 | 13 | 16 | 15 | 7 | 10 | 9 | 8 | 11 | 5 | 6 | 3 | 2 | 1 | 4 |
| 13 | 2 | 4 | 1 | 3 | 8 | 5 | 10 | 11 | 12 | 9 | 6 | 7 | 14 | 15 | 0 | 17 | 19 | 16 | 18 | 22 | 23 | 21 | 20 |
| 14 | 4 | 3 | 2 | 1 | 11 | 8 | 9 | 6 | 7 | 12 | 5 | 10 | 15 | 0 | 13 | 19 | 18 | 17 | 16 | 21 | 20 | 23 | 22 |
| 15 | 3 | 1 | 4 | 2 | 6 | 11 | 12 | 5 | 10 | 7 | 8 | 9 | 0 | 13 | 14 | 18 | 16 | 19 | 17 | 23 | 22 | 20 | 21 |
| 16 | 5 | 8 | 6 | 11 | 7 | 12 | 2 | 10 | 3 | 4 | 9 | 1 | 17 | 19 | 18 | 20 | 22 | 23 | 21 | 13 | 15 | 14 | 0 |
| 17 | 8 | 11 | 5 | 6 | 10 | 7 | 4 | 9 | 1 | 3 | 12 | 2 | 19 | 18 | 16 | 22 | 21 | 20 | 23 | 14 | 0 | 15 | 13 |
| 18 | 6 | 5 | 11 | 8 | 12 | 9 | 1 | 7 | 4 | 2 | 10 | 3 | 16 | 17 | 19 | 23 | 20 | 21 | 22 | 0 | 14 | 13 | 15 |
| 19 | 11 | 6 | 8 | 5 | 9 | 10 | 3 | 12 | 2 | 1 | 7 | 4 | 18 | 16 | 17 | 21 | 23 | 22 | 20 | 15 | 13 | 0 | 14 |
| 20 | 7 | 10 | 12 | 9 | 2 | 1 | 8 | 4 | 6 | 11 | 3 | 5 | 22 | 21 | 23 | 13 | 14 | 0 | 15 | 17 | 18 | 19 | 16 |
| 21 | 9 | 12 | 10 | 7 | 3 | 4 | 6 | 1 | 8 | 5 | 2 | 11 | 23 | 20 | 22 | 15 | 0 | 14 | 13 | 18 | 17 | 16 | 19 |
| 22 | 10 | 9 | 7 | 12 | 4 | 2 | 11 | 3 | 5 | 6 | 1 | 8 | 21 | 23 | 20 | 14 | 15 | 13 | 0 | 19 | 16 | 18 | 17 |
| 23 | 12 | 7 | 9 | 10 | 1 | 3 | 5 | 2 | 11 | 8 | 4 | 6 | 20 | 22 | 21 | 0 | 13 | 15 | 14 | 16 | 19 | 17 | 18 |
Centre: 0 13 14 15
Centrum: 0 13 14 15
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
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
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
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
1 Element of order 1: 0
1 Element of order 2: 14
2 Elements of order 3: 17 21
2 Elements of order 4: 13 15
2 Elements of order 6: 18 20
12 Elements of order 8: 1 2 3 4 5 6 7 8 9 10 11 12
4 Elements of order 12: 16 19 22 23
Commutator Subloop: 0 17 21
Associator Subloop: 0
4 Conjugacy Classes of size 1:
4 Conjugacy Classes of size 2:
4 Conjugacy Classes of size 3:
Automorphic Inverse Property: FAILS. (1-1)(6-1) neq (1*6)-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: 24 (24, 144)
/ revised November, 2001