| 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 | 5 | 0 | 3 | 4 | 7 | 11 | 6 | 8 | 9 | 10 | 13 | 17 | 12 | 14 | 15 | 16 | 19 | 20 | 21 | 22 | 23 | 18 |
| 2 | 5 | 4 | 1 | 0 | 3 | 11 | 10 | 7 | 6 | 8 | 9 | 17 | 16 | 13 | 12 | 14 | 15 | 20 | 21 | 22 | 23 | 18 | 19 |
| 3 | 0 | 1 | 4 | 5 | 2 | 8 | 6 | 9 | 10 | 11 | 7 | 14 | 12 | 15 | 16 | 17 | 13 | 23 | 18 | 19 | 20 | 21 | 22 |
| 4 | 3 | 0 | 5 | 2 | 1 | 9 | 8 | 10 | 11 | 7 | 6 | 15 | 14 | 16 | 17 | 13 | 12 | 22 | 23 | 18 | 19 | 20 | 21 |
| 5 | 4 | 3 | 2 | 1 | 0 | 10 | 9 | 11 | 7 | 6 | 8 | 16 | 15 | 17 | 13 | 12 | 14 | 21 | 22 | 23 | 18 | 19 | 20 |
| 6 | 8 | 9 | 7 | 11 | 10 | 0 | 3 | 1 | 2 | 5 | 4 | 18 | 19 | 23 | 22 | 21 | 20 | 15 | 14 | 12 | 13 | 17 | 16 |
| 7 | 6 | 8 | 11 | 10 | 9 | 1 | 0 | 2 | 5 | 4 | 3 | 23 | 18 | 22 | 21 | 20 | 19 | 16 | 15 | 14 | 12 | 13 | 17 |
| 8 | 9 | 10 | 6 | 7 | 11 | 3 | 4 | 0 | 1 | 2 | 5 | 19 | 20 | 18 | 23 | 22 | 21 | 14 | 12 | 13 | 17 | 16 | 15 |
| 9 | 10 | 11 | 8 | 6 | 7 | 4 | 5 | 3 | 0 | 1 | 2 | 20 | 21 | 19 | 18 | 23 | 22 | 12 | 13 | 17 | 16 | 15 | 14 |
| 10 | 11 | 7 | 9 | 8 | 6 | 5 | 2 | 4 | 3 | 0 | 1 | 21 | 22 | 20 | 19 | 18 | 23 | 13 | 17 | 16 | 15 | 14 | 12 |
| 11 | 7 | 6 | 10 | 9 | 8 | 2 | 1 | 5 | 4 | 3 | 0 | 22 | 23 | 21 | 20 | 19 | 18 | 17 | 16 | 15 | 14 | 12 | 13 |
| 12 | 14 | 15 | 13 | 17 | 16 | 23 | 18 | 22 | 21 | 20 | 19 | 0 | 3 | 1 | 2 | 5 | 4 | 9 | 8 | 6 | 7 | 11 | 10 |
| 13 | 12 | 14 | 17 | 16 | 15 | 22 | 23 | 21 | 20 | 19 | 18 | 1 | 0 | 2 | 5 | 4 | 3 | 10 | 9 | 8 | 6 | 7 | 11 |
| 14 | 15 | 16 | 12 | 13 | 17 | 18 | 19 | 23 | 22 | 21 | 20 | 3 | 4 | 0 | 1 | 2 | 5 | 8 | 6 | 7 | 11 | 10 | 9 |
| 15 | 16 | 17 | 14 | 12 | 13 | 19 | 20 | 18 | 23 | 22 | 21 | 4 | 5 | 3 | 0 | 1 | 2 | 6 | 7 | 11 | 10 | 9 | 8 |
| 16 | 17 | 13 | 15 | 14 | 12 | 20 | 21 | 19 | 18 | 23 | 22 | 5 | 2 | 4 | 3 | 0 | 1 | 7 | 11 | 10 | 9 | 8 | 6 |
| 17 | 13 | 12 | 16 | 15 | 14 | 21 | 22 | 20 | 19 | 18 | 23 | 2 | 1 | 5 | 4 | 3 | 0 | 11 | 10 | 9 | 8 | 6 | 7 |
| 18 | 23 | 22 | 19 | 20 | 21 | 14 | 12 | 15 | 16 | 17 | 13 | 6 | 7 | 8 | 9 | 10 | 11 | 0 | 3 | 4 | 5 | 2 | 1 |
| 19 | 18 | 23 | 20 | 21 | 22 | 15 | 14 | 16 | 17 | 13 | 12 | 8 | 6 | 9 | 10 | 11 | 7 | 1 | 0 | 3 | 4 | 5 | 2 |
| 20 | 19 | 18 | 21 | 22 | 23 | 16 | 15 | 17 | 13 | 12 | 14 | 9 | 8 | 10 | 11 | 7 | 6 | 2 | 1 | 0 | 3 | 4 | 5 |
| 21 | 20 | 19 | 22 | 23 | 18 | 17 | 16 | 13 | 12 | 14 | 15 | 10 | 9 | 11 | 7 | 6 | 8 | 5 | 2 | 1 | 0 | 3 | 4 |
| 22 | 21 | 20 | 23 | 18 | 19 | 13 | 17 | 12 | 14 | 15 | 16 | 11 | 10 | 7 | 6 | 8 | 9 | 4 | 5 | 2 | 1 | 0 | 3 |
| 23 | 22 | 21 | 18 | 19 | 20 | 12 | 13 | 14 | 15 | 16 | 17 | 7 | 11 | 6 | 8 | 9 | 10 | 3 | 4 | 5 | 2 | 1 | 0 |
Centre: 0 5
Centrum: 0 5
Nucleus: 0 5
Left Nucleus: 0 5 8 11
Middle Nucleus: 0 1 2 3 4 5
Right Nucleus: 0 1 2 3 4 5
1 Element of order 1: 0
19 Elements of order 2: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
2 Elements of order 3: 2 4
2 Elements of order 6: 1 3
Commutator Subloop: 0 1 2 3 4 5
Associator Subloop: 0 1 2 3 4 5
2 Conjugacy Classes of size 1:
2 Conjugacy Classes of size 2:
3 Conjugacy Classes of size 6:
Automorphic Inverse Property: FAILS. (1-1)(7-1) neq (1*7)-1
Al Property: FAILS. The left inner mapping L6,1 = (12,17,15)(13,16,14)(18,20,22)(19,21,23) is not an automorphism. L6,1(12*6) neq L6,1(12)*L6,1(6)
Ar Property: HOLDS (i.e. every right inner mapping Ra,b is an automorphism)
Right (Left, Full) Mult Group Orders: 48 (2592, 10368)
/ revised November, 2001