Moufang Loop 20.15.1.1 of order 20

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
1	4	0	2	3	8	9	5	6	7	16	15	18	17	10	19	12	11	14	13
2	0	3	4	1	7	8	9	5	6	14	17	16	19	18	11	10	13	12	15
3	2	4	1	0	9	5	6	7	8	18	13	10	15	12	17	14	19	16	11
4	3	1	0	2	6	7	8	9	5	12	19	14	11	16	13	18	15	10	17
5	7	8	6	9	0	3	1	2	4	13	18	15	10	17	12	19	14	11	16
6	8	9	7	5	4	0	3	1	2	15	16	17	18	19	10	11	12	13	14
7	9	5	8	6	2	4	0	3	1	17	14	19	16	11	18	13	10	15	12
8	5	6	9	7	1	2	4	0	3	19	12	11	14	13	16	15	18	17	10
9	6	7	5	8	3	1	2	4	0	11	10	13	12	15	14	17	16	19	18
10	14	16	12	18	13	15	17	19	11	0	9	3	5	1	6	2	7	4	8
11	17	15	19	13	18	16	14	12	10	9	0	8	4	7	2	6	1	5	3
12	16	18	14	10	15	17	19	11	13	4	8	0	9	3	5	1	6	2	7
13	19	17	11	15	10	18	16	14	12	5	3	9	0	8	4	7	2	6	1
14	18	10	16	12	17	19	11	13	15	2	7	4	8	0	9	3	5	1	6
15	11	19	13	17	12	10	18	16	14	6	1	5	3	9	0	8	4	7	2
16	10	12	18	14	19	11	13	15	17	1	6	2	7	4	8	0	9	3	5
17	13	11	15	19	14	12	10	18	16	7	2	6	1	5	3	9	0	8	4
18	12	14	10	16	11	13	15	17	19	3	5	1	6	2	7	4	8	0	9
19	15	13	17	11	16	14	12	10	18	8	4	7	2	6	1	5	3	9	0

Centre: 0

Centrum: 0

Nucleus: 0

Left Nucleus: 0

Middle Nucleus: 0

Right Nucleus: 0

1 Element of order 1: 0

15 Elements of order 2: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

4 Elements of order 5: 1 2 3 4

Commutator Subloop: 0 1 2 3 4

Associator Subloop: 0 1 2 3 4

1 Conjugacy Class of size 1:

2 Conjugacy Classes of size 2:

3 Conjugacy Classes of size 5:

5 6 7 8 9
10 12 14 16 18
11 13 15 17 19

Automorphic Inverse Property: FAILS. (1^-1)(6^-1) neq (1*6)^-1

A_l Property: FAILS. The left inner mapping L_1,5 = (10,12,14,16,18)(11,19,17,15,13) is not an automorphism. L_1,5(5*10) neq L_1,5(5)*L_1,5(10)

A_r Property: FAILS. The right inner mapping R_1,5 = (10,18,16,14,12)(11,13,15,17,19) is not an automorphism. R_1,5(5*10) neq R_1,5(5)*R_1,5(10)

Right (Left, Full) Mult Group Orders: 5000 (5000, 20000)

/ revised November, 2001

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
1	4	0	2	3	8	9	5	6	7	16	15	18	17	10	19	12	11	14	13
2	0	3	4	1	7	8	9	5	6	14	17	16	19	18	11	10	13	12	15
3	2	4	1	0	9	5	6	7	8	18	13	10	15	12	17	14	19	16	11
4	3	1	0	2	6	7	8	9	5	12	19	14	11	16	13	18	15	10	17
5	7	8	6	9	0	3	1	2	4	13	18	15	10	17	12	19	14	11	16
6	8	9	7	5	4	0	3	1	2	15	16	17	18	19	10	11	12	13	14
7	9	5	8	6	2	4	0	3	1	17	14	19	16	11	18	13	10	15	12
8	5	6	9	7	1	2	4	0	3	19	12	11	14	13	16	15	18	17	10
9	6	7	5	8	3	1	2	4	0	11	10	13	12	15	14	17	16	19	18
10	14	16	12	18	13	15	17	19	11	0	9	3	5	1	6	2	7	4	8
11	17	15	19	13	18	16	14	12	10	9	0	8	4	7	2	6	1	5	3
12	16	18	14	10	15	17	19	11	13	4	8	0	9	3	5	1	6	2	7
13	19	17	11	15	10	18	16	14	12	5	3	9	0	8	4	7	2	6	1
14	18	10	16	12	17	19	11	13	15	2	7	4	8	0	9	3	5	1	6
15	11	19	13	17	12	10	18	16	14	6	1	5	3	9	0	8	4	7	2
16	10	12	18	14	19	11	13	15	17	1	6	2	7	4	8	0	9	3	5
17	13	11	15	19	14	12	10	18	16	7	2	6	1	5	3	9	0	8	4
18	12	14	10	16	11	13	15	17	19	3	5	1	6	2	7	4	8	0	9
19	15	13	17	11	16	14	12	10	18	8	4	7	2	6	1	5	3	9	0

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
1	4	0	2	3	8	9	5	6	7	16	15	18	17	10	19	12	11	14	13
2	0	3	4	1	7	8	9	5	6	14	17	16	19	18	11	10	13	12	15
3	2	4	1	0	9	5	6	7	8	18	13	10	15	12	17	14	19	16	11
4	3	1	0	2	6	7	8	9	5	12	19	14	11	16	13	18	15	10	17
5	7	8	6	9	0	3	1	2	4	13	18	15	10	17	12	19	14	11	16
6	8	9	7	5	4	0	3	1	2	15	16	17	18	19	10	11	12	13	14
7	9	5	8	6	2	4	0	3	1	17	14	19	16	11	18	13	10	15	12
8	5	6	9	7	1	2	4	0	3	19	12	11	14	13	16	15	18	17	10
9	6	7	5	8	3	1	2	4	0	11	10	13	12	15	14	17	16	19	18
10	14	16	12	18	13	15	17	19	11	0	9	3	5	1	6	2	7	4	8
11	17	15	19	13	18	16	14	12	10	9	0	8	4	7	2	6	1	5	3
12	16	18	14	10	15	17	19	11	13	4	8	0	9	3	5	1	6	2	7
13	19	17	11	15	10	18	16	14	12	5	3	9	0	8	4	7	2	6	1
14	18	10	16	12	17	19	11	13	15	2	7	4	8	0	9	3	5	1	6
15	11	19	13	17	12	10	18	16	14	6	1	5	3	9	0	8	4	7	2
16	10	12	18	14	19	11	13	15	17	1	6	2	7	4	8	0	9	3	5
17	13	11	15	19	14	12	10	18	16	7	2	6	1	5	3	9	0	8	4
18	12	14	10	16	11	13	15	17	19	3	5	1	6	2	7	4	8	0	9
19	15	13	17	11	16	14	12	10	18	8	4	7	2	6	1	5	3	9	0

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
1	4	0	2	3	8	9	5	6	7	16	15	18	17	10	19	12	11	14	13
2	0	3	4	1	7	8	9	5	6	14	17	16	19	18	11	10	13	12	15
3	2	4	1	0	9	5	6	7	8	18	13	10	15	12	17	14	19	16	11
4	3	1	0	2	6	7	8	9	5	12	19	14	11	16	13	18	15	10	17
5	7	8	6	9	0	3	1	2	4	13	18	15	10	17	12	19	14	11	16
6	8	9	7	5	4	0	3	1	2	15	16	17	18	19	10	11	12	13	14
7	9	5	8	6	2	4	0	3	1	17	14	19	16	11	18	13	10	15	12
8	5	6	9	7	1	2	4	0	3	19	12	11	14	13	16	15	18	17	10
9	6	7	5	8	3	1	2	4	0	11	10	13	12	15	14	17	16	19	18
10	14	16	12	18	13	15	17	19	11	0	9	3	5	1	6	2	7	4	8
11	17	15	19	13	18	16	14	12	10	9	0	8	4	7	2	6	1	5	3
12	16	18	14	10	15	17	19	11	13	4	8	0	9	3	5	1	6	2	7
13	19	17	11	15	10	18	16	14	12	5	3	9	0	8	4	7	2	6	1
14	18	10	16	12	17	19	11	13	15	2	7	4	8	0	9	3	5	1	6
15	11	19	13	17	12	10	18	16	14	6	1	5	3	9	0	8	4	7	2
16	10	12	18	14	19	11	13	15	17	1	6	2	7	4	8	0	9	3	5
17	13	11	15	19	14	12	10	18	16	7	2	6	1	5	3	9	0	8	4
18	12	14	10	16	11	13	15	17	19	3	5	1	6	2	7	4	8	0	9
19	15	13	17	11	16	14	12	10	18	8	4	7	2	6	1	5	3	9	0