| 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 | 2 | 3 | 0 | 5 | 9 | 18 | 4 | 17 | 7 | 11 | 13 | 10 | 12 | 19 | 16 | 14 | 6 | 8 | 15 | 22 | 23 | 21 | 20 |
| 2 | 3 | 0 | 1 | 9 | 7 | 8 | 5 | 6 | 4 | 13 | 12 | 11 | 10 | 15 | 14 | 19 | 18 | 17 | 16 | 21 | 20 | 23 | 22 |
| 3 | 0 | 1 | 2 | 7 | 4 | 17 | 9 | 18 | 5 | 12 | 10 | 13 | 11 | 16 | 19 | 15 | 8 | 6 | 14 | 23 | 22 | 20 | 21 |
| 4 | 6 | 9 | 8 | 10 | 19 | 14 | 16 | 15 | 13 | 0 | 20 | 21 | 2 | 1 | 3 | 22 | 11 | 12 | 23 | 17 | 18 | 7 | 5 |
| 5 | 18 | 7 | 17 | 11 | 15 | 19 | 14 | 16 | 12 | 1 | 22 | 23 | 3 | 2 | 0 | 21 | 13 | 10 | 20 | 6 | 8 | 4 | 9 |
| 6 | 9 | 8 | 4 | 19 | 13 | 12 | 10 | 11 | 16 | 20 | 2 | 0 | 21 | 23 | 22 | 1 | 14 | 15 | 3 | 7 | 5 | 18 | 17 |
| 7 | 17 | 5 | 18 | 12 | 14 | 16 | 15 | 19 | 11 | 3 | 23 | 22 | 1 | 0 | 2 | 20 | 10 | 13 | 21 | 8 | 6 | 9 | 4 |
| 8 | 4 | 6 | 9 | 16 | 10 | 11 | 13 | 12 | 19 | 21 | 0 | 2 | 20 | 22 | 23 | 3 | 15 | 14 | 1 | 5 | 7 | 17 | 18 |
| 9 | 8 | 4 | 6 | 13 | 16 | 15 | 19 | 14 | 10 | 2 | 21 | 20 | 0 | 3 | 1 | 23 | 12 | 11 | 22 | 18 | 17 | 5 | 7 |
| 10 | 14 | 13 | 15 | 0 | 23 | 1 | 22 | 3 | 2 | 4 | 17 | 18 | 9 | 6 | 8 | 7 | 20 | 21 | 5 | 11 | 12 | 16 | 19 |
| 11 | 19 | 12 | 16 | 1 | 20 | 2 | 21 | 0 | 3 | 5 | 6 | 8 | 7 | 18 | 17 | 4 | 22 | 23 | 9 | 13 | 10 | 14 | 15 |
| 12 | 16 | 11 | 19 | 3 | 21 | 0 | 20 | 2 | 1 | 7 | 8 | 6 | 5 | 17 | 18 | 9 | 23 | 22 | 4 | 10 | 13 | 15 | 14 |
| 13 | 15 | 10 | 14 | 2 | 22 | 3 | 23 | 1 | 0 | 9 | 18 | 17 | 4 | 8 | 6 | 5 | 21 | 20 | 7 | 12 | 11 | 19 | 16 |
| 14 | 13 | 15 | 10 | 23 | 2 | 21 | 0 | 20 | 22 | 17 | 9 | 4 | 18 | 5 | 7 | 6 | 1 | 3 | 8 | 16 | 19 | 12 | 11 |
| 15 | 10 | 14 | 13 | 22 | 0 | 20 | 2 | 21 | 23 | 18 | 4 | 9 | 17 | 7 | 5 | 8 | 3 | 1 | 6 | 19 | 16 | 11 | 12 |
| 16 | 11 | 19 | 12 | 21 | 1 | 22 | 3 | 23 | 20 | 8 | 5 | 7 | 6 | 4 | 9 | 17 | 0 | 2 | 18 | 15 | 14 | 13 | 10 |
| 17 | 5 | 18 | 7 | 14 | 11 | 13 | 12 | 10 | 15 | 23 | 1 | 3 | 22 | 21 | 20 | 0 | 16 | 19 | 2 | 9 | 4 | 6 | 8 |
| 18 | 7 | 17 | 5 | 15 | 12 | 10 | 11 | 13 | 14 | 22 | 3 | 1 | 23 | 20 | 21 | 2 | 19 | 16 | 0 | 4 | 9 | 8 | 6 |
| 19 | 12 | 16 | 11 | 20 | 3 | 23 | 1 | 22 | 21 | 6 | 7 | 5 | 8 | 9 | 4 | 18 | 2 | 0 | 17 | 14 | 15 | 10 | 13 |
| 20 | 23 | 21 | 22 | 6 | 17 | 9 | 18 | 4 | 8 | 19 | 14 | 15 | 16 | 12 | 11 | 10 | 7 | 5 | 13 | 2 | 0 | 1 | 3 |
| 21 | 22 | 20 | 23 | 8 | 18 | 4 | 17 | 9 | 6 | 16 | 15 | 14 | 19 | 11 | 12 | 13 | 5 | 7 | 10 | 0 | 2 | 3 | 1 |
| 22 | 20 | 23 | 21 | 18 | 6 | 7 | 8 | 5 | 17 | 15 | 19 | 16 | 14 | 10 | 13 | 11 | 4 | 9 | 12 | 3 | 1 | 2 | 0 |
| 23 | 21 | 22 | 20 | 17 | 8 | 5 | 6 | 7 | 18 | 14 | 16 | 19 | 15 | 13 | 10 | 12 | 9 | 4 | 11 | 1 | 3 | 0 | 2 |
Centre: 0 2
Centrum: 0 2
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: 2
8 Elements of order 3: 4 5 6 10 12 15 16 17
6 Elements of order 4: 1 3 20 21 22 23
8 Elements of order 6: 7 8 9 11 13 14 18 19
Commutator Subloop: 0 1 2 3 20 21 22 23
Associator Subloop: 0
2 Conjugacy Classes of size 1:
4 Conjugacy Classes of size 4:
1 Conjugacy Class of size 6:
Automorphic Inverse Property: FAILS. (1-1)(5-1) neq (1*5)-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, 288)
/ revised November, 2001