0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
1 | 4 | 0 | 2 | 6 | 3 | 5 | 13 | 7 | 8 | 9 | 10 | 11 | 12 | 17 | 18 | 14 | 19 | 16 | 20 | 15 |
2 | 0 | 3 | 5 | 1 | 6 | 4 | 8 | 9 | 10 | 11 | 12 | 13 | 7 | 16 | 20 | 18 | 14 | 15 | 17 | 19 |
3 | 2 | 5 | 6 | 0 | 4 | 1 | 9 | 10 | 11 | 12 | 13 | 7 | 8 | 18 | 19 | 15 | 16 | 20 | 14 | 17 |
4 | 6 | 1 | 0 | 5 | 2 | 3 | 12 | 13 | 7 | 8 | 9 | 10 | 11 | 19 | 16 | 17 | 20 | 14 | 15 | 18 |
5 | 3 | 6 | 4 | 2 | 1 | 0 | 10 | 11 | 12 | 13 | 7 | 8 | 9 | 15 | 17 | 20 | 18 | 19 | 16 | 14 |
6 | 5 | 4 | 1 | 3 | 0 | 2 | 11 | 12 | 13 | 7 | 8 | 9 | 10 | 20 | 14 | 19 | 15 | 17 | 18 | 16 |
7 | 9 | 12 | 10 | 11 | 8 | 13 | 16 | 18 | 15 | 20 | 19 | 17 | 14 | 6 | 1 | 0 | 2 | 5 | 4 | 3 |
8 | 10 | 13 | 11 | 12 | 9 | 7 | 18 | 15 | 20 | 19 | 17 | 14 | 16 | 4 | 0 | 2 | 3 | 6 | 1 | 5 |
9 | 11 | 7 | 12 | 13 | 10 | 8 | 15 | 20 | 19 | 17 | 14 | 16 | 18 | 1 | 2 | 3 | 5 | 4 | 0 | 6 |
10 | 12 | 8 | 13 | 7 | 11 | 9 | 20 | 19 | 17 | 14 | 16 | 18 | 15 | 0 | 3 | 5 | 6 | 1 | 2 | 4 |
11 | 13 | 9 | 7 | 8 | 12 | 10 | 19 | 17 | 14 | 16 | 18 | 15 | 20 | 2 | 5 | 6 | 4 | 0 | 3 | 1 |
12 | 7 | 10 | 8 | 9 | 13 | 11 | 17 | 14 | 16 | 18 | 15 | 20 | 19 | 3 | 6 | 4 | 1 | 2 | 5 | 0 |
13 | 8 | 11 | 9 | 10 | 7 | 12 | 14 | 16 | 18 | 15 | 20 | 19 | 17 | 5 | 4 | 1 | 0 | 3 | 6 | 2 |
14 | 17 | 16 | 18 | 19 | 15 | 20 | 1 | 6 | 3 | 0 | 4 | 5 | 2 | 10 | 12 | 13 | 7 | 9 | 11 | 8 |
15 | 18 | 20 | 19 | 16 | 17 | 14 | 3 | 0 | 4 | 5 | 2 | 1 | 6 | 13 | 8 | 9 | 10 | 12 | 7 | 11 |
16 | 14 | 18 | 15 | 17 | 20 | 19 | 0 | 4 | 5 | 2 | 1 | 6 | 3 | 11 | 13 | 7 | 8 | 10 | 12 | 9 |
17 | 19 | 14 | 16 | 20 | 18 | 15 | 4 | 5 | 2 | 1 | 6 | 3 | 0 | 9 | 11 | 12 | 13 | 8 | 10 | 7 |
18 | 16 | 15 | 20 | 14 | 19 | 17 | 2 | 1 | 6 | 3 | 0 | 4 | 5 | 12 | 7 | 8 | 9 | 11 | 13 | 10 |
19 | 20 | 17 | 14 | 15 | 16 | 18 | 6 | 3 | 0 | 4 | 5 | 2 | 1 | 8 | 10 | 11 | 12 | 7 | 9 | 13 |
20 | 15 | 19 | 17 | 18 | 14 | 16 | 5 | 2 | 1 | 6 | 3 | 0 | 4 | 7 | 9 | 10 | 11 | 13 | 8 | 12 |
Centre: 0
Centrum: 0
Nucleus: 0
Left Nucleus: 0 1 2 3 4 5 6
Middle Nucleus: 0
Right Nucleus: 0
1 Element of order 1: 0
14 Elements of order 3: 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6 Elements of order 7: 1 2 3 4 5 6
Commutator Subloop: 0 1 2 3 4 5 6
Associator Subloop: 0 1 2 3 4 5 6
1 Conjugacy Class of size 1:
1 Conjugacy Class of size 6:
2 Conjugacy Classes of size 7:
Automorphic Inverse Property: FAILS. (1-1)(8-1) neq (1*8)-1
Al Property: FAILS. The left inner mapping L1,7 = (7,11,8,12,9,13,10)(14,15,17,18,19,16,20) is not an automorphism. L1,7(7*7) neq L1,7(7)*L1,7(7)
Ar Property: FAILS. The right inner mapping R1,7 = (7,10,13,9,12,8,11)(14,20,16,19,18,17,15) is not an automorphism. R1,7(7*7) neq R1,7(7)*R1,7(7)
Right (Left, Full) Mult Group Orders: 147 (12348, 37044)