| 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 | 0 | 4 | 5 | 3 | 7 | 8 | 6 | 10 | 11 | 9 | 13 | 14 | 12 | 17 | 15 | 16 | 19 | 23 | 21 | 22 | 20 | 18 |
| 2 | 0 | 1 | 5 | 3 | 4 | 8 | 6 | 7 | 11 | 9 | 10 | 14 | 12 | 13 | 16 | 17 | 15 | 23 | 18 | 22 | 20 | 21 | 19 |
| 3 | 5 | 4 | 0 | 2 | 1 | 9 | 10 | 11 | 6 | 7 | 8 | 15 | 17 | 16 | 12 | 14 | 13 | 21 | 22 | 23 | 18 | 19 | 20 |
| 4 | 3 | 5 | 1 | 0 | 2 | 11 | 9 | 10 | 8 | 6 | 7 | 16 | 15 | 17 | 14 | 13 | 12 | 20 | 21 | 19 | 23 | 18 | 22 |
| 5 | 4 | 3 | 2 | 1 | 0 | 10 | 11 | 9 | 7 | 8 | 6 | 17 | 16 | 15 | 13 | 12 | 14 | 22 | 20 | 18 | 19 | 23 | 21 |
| 6 | 8 | 7 | 10 | 11 | 9 | 0 | 2 | 1 | 3 | 4 | 5 | 18 | 19 | 23 | 21 | 20 | 22 | 13 | 14 | 15 | 17 | 16 | 12 |
| 7 | 6 | 8 | 9 | 10 | 11 | 1 | 0 | 2 | 5 | 3 | 4 | 23 | 18 | 19 | 20 | 22 | 21 | 12 | 13 | 16 | 15 | 17 | 14 |
| 8 | 7 | 6 | 11 | 9 | 10 | 2 | 1 | 0 | 4 | 5 | 3 | 19 | 23 | 18 | 22 | 21 | 20 | 14 | 12 | 17 | 16 | 15 | 13 |
| 9 | 11 | 10 | 7 | 8 | 6 | 3 | 4 | 5 | 0 | 2 | 1 | 21 | 22 | 20 | 18 | 23 | 19 | 17 | 16 | 12 | 13 | 14 | 15 |
| 10 | 9 | 11 | 6 | 7 | 8 | 5 | 3 | 4 | 1 | 0 | 2 | 20 | 21 | 22 | 23 | 19 | 18 | 15 | 17 | 14 | 12 | 13 | 16 |
| 11 | 10 | 9 | 8 | 6 | 7 | 4 | 5 | 3 | 2 | 1 | 0 | 22 | 20 | 21 | 19 | 18 | 23 | 16 | 15 | 13 | 14 | 12 | 17 |
| 12 | 14 | 13 | 16 | 15 | 17 | 19 | 23 | 18 | 22 | 20 | 21 | 0 | 2 | 1 | 3 | 5 | 4 | 7 | 8 | 9 | 10 | 11 | 6 |
| 13 | 12 | 14 | 17 | 16 | 15 | 18 | 19 | 23 | 21 | 22 | 20 | 1 | 0 | 2 | 5 | 4 | 3 | 6 | 7 | 11 | 9 | 10 | 8 |
| 14 | 13 | 12 | 15 | 17 | 16 | 23 | 18 | 19 | 20 | 21 | 22 | 2 | 1 | 0 | 4 | 3 | 5 | 8 | 6 | 10 | 11 | 9 | 7 |
| 15 | 16 | 17 | 14 | 12 | 13 | 22 | 20 | 21 | 19 | 23 | 18 | 3 | 4 | 5 | 0 | 1 | 2 | 10 | 11 | 6 | 7 | 8 | 9 |
| 16 | 17 | 15 | 12 | 13 | 14 | 20 | 21 | 22 | 23 | 18 | 19 | 4 | 5 | 3 | 2 | 0 | 1 | 11 | 9 | 7 | 8 | 6 | 10 |
| 17 | 15 | 16 | 13 | 14 | 12 | 21 | 22 | 20 | 18 | 19 | 23 | 5 | 3 | 4 | 1 | 2 | 0 | 9 | 10 | 8 | 6 | 7 | 11 |
| 18 | 23 | 19 | 22 | 20 | 21 | 13 | 14 | 12 | 17 | 16 | 15 | 6 | 7 | 8 | 9 | 11 | 10 | 0 | 2 | 5 | 3 | 4 | 1 |
| 19 | 18 | 23 | 21 | 22 | 20 | 12 | 13 | 14 | 15 | 17 | 16 | 8 | 6 | 7 | 11 | 10 | 9 | 1 | 0 | 4 | 5 | 3 | 2 |
| 20 | 22 | 21 | 23 | 18 | 19 | 16 | 15 | 17 | 14 | 12 | 13 | 10 | 11 | 9 | 7 | 6 | 8 | 4 | 5 | 0 | 2 | 1 | 3 |
| 21 | 20 | 22 | 19 | 23 | 18 | 17 | 16 | 15 | 13 | 14 | 12 | 9 | 10 | 11 | 6 | 8 | 7 | 3 | 4 | 1 | 0 | 2 | 5 |
| 22 | 21 | 20 | 18 | 19 | 23 | 15 | 17 | 16 | 12 | 13 | 14 | 11 | 9 | 10 | 8 | 7 | 6 | 5 | 3 | 2 | 1 | 0 | 4 |
| 23 | 19 | 18 | 20 | 21 | 22 | 14 | 12 | 13 | 16 | 15 | 17 | 7 | 8 | 6 | 10 | 9 | 11 | 2 | 1 | 3 | 4 | 5 | 0 |
Centre: 0
Centrum: 0
Nucleus: 0
Left Nucleus: 0 3 8 11 13 17 20 23
Middle Nucleus: 0 1 2
Right Nucleus: 0 1 2
1 Element of order 1: 0
21 Elements of order 2: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
2 Elements of order 3: 1 2
Commutator Subloop: 0 1 2
Associator Subloop: 0 1 2
1 Conjugacy Class of size 1:
1 Conjugacy Class of size 2:
7 Conjugacy Classes of size 3:
Automorphic Inverse Property: FAILS. (1-1)(4-1) neq (1*4)-1
Al Property: FAILS. The left inner mapping L3,1 = (6,8,7)(9,11,10)(12,14,13)(15,16,17)(18,23,19)(20,22,21) is not an automorphism. L3,1(6*3) neq L3,1(6)*L3,1(3)
Ar Property: HOLDS (i.e. every right inner mapping Ra,b is an automorphism)
Right (Left, Full) Mult Group Orders: 48 (17496, 104976)
/ revised November, 2001