Moufang Loop 24.19.2.2 of order 24

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	21	23	22	20	18
2	5	4	1	0	3	11	10	7	6	8	9	17	16	13	12	14	15	21	22	18	20	23	19
3	0	1	4	5	2	8	6	9	10	11	7	14	12	15	16	17	13	23	18	22	19	21	20
4	3	0	5	2	1	9	8	10	11	7	6	15	14	16	17	13	12	20	23	21	18	19	22
5	4	3	2	1	0	10	9	11	7	6	8	16	15	17	13	12	14	22	20	19	23	18	21
6	8	9	7	11	10	0	3	1	2	5	4	18	23	19	21	22	20	12	14	17	15	16	13
7	6	8	11	10	9	1	0	2	5	4	3	23	20	18	19	21	22	14	15	13	16	17	12
8	9	10	6	7	11	3	4	0	1	2	5	19	18	21	22	20	23	13	12	16	14	15	17
9	10	11	8	6	7	4	5	3	0	1	2	21	19	22	20	23	18	17	13	15	12	14	16
10	11	7	9	8	6	5	2	4	3	0	1	22	21	20	23	18	19	16	17	14	13	12	15
11	7	6	10	9	8	2	1	5	4	3	0	20	22	23	18	19	21	15	16	12	17	13	14
12	14	15	13	17	16	18	23	19	21	22	20	0	3	1	2	5	4	6	8	11	9	10	7
13	12	14	17	16	15	23	20	18	19	21	22	1	0	2	5	4	3	8	9	7	10	11	6
14	15	16	12	13	17	19	18	21	22	20	23	3	4	0	1	2	5	7	6	10	8	9	11
15	16	17	14	12	13	21	19	22	20	23	18	4	5	3	0	1	2	11	7	9	6	8	10
16	17	13	15	14	12	22	21	20	23	18	19	5	2	4	3	0	1	10	11	8	7	6	9
17	13	12	16	15	14	20	22	23	18	19	21	2	1	5	4	3	0	9	10	6	11	7	8
18	23	20	19	21	22	12	14	13	17	16	15	6	8	7	11	10	9	0	3	2	4	5	1
19	18	23	21	22	20	14	15	12	13	17	16	8	9	6	7	11	10	1	0	5	3	4	2
20	22	21	23	18	19	17	13	16	15	14	12	11	7	10	9	8	6	4	5	0	2	1	3
21	19	18	22	20	23	15	16	14	12	13	17	9	10	8	6	7	11	2	1	4	0	3	5
22	21	19	20	23	18	16	17	15	14	12	13	10	11	9	8	6	7	5	2	3	1	0	4
23	20	22	18	19	21	13	12	17	16	15	14	7	6	11	10	9	8	3	4	1	5	2	0

Centre: 0 5

Centrum: 0 5

Nucleus: 0 5

Left Nucleus: 0 5

Middle Nucleus: 0 5

Right Nucleus: 0 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 2 4

Associator Subloop: 0 2 4

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

6 Conjugacy Classes of size 3:

6 9 11
7 8 10
12 15 17
13 14 16
18 20 21
19 22 23

Automorphic Inverse Property: FAILS. (1^-1)(7^-1) neq (1*7)^-1

A_l Property: FAILS. The left inner mapping L_1,6 = (12,17,15)(13,16,14)(18,21,20)(19,22,23) is not an automorphism. L_1,6(6*12) neq L_1,6(6)*L_1,6(12)

A_r Property: FAILS. The right inner mapping R_1,6 = (12,15,17)(13,14,16)(18,20,21)(19,23,22) is not an automorphism. R_1,6(6*12) neq R_1,6(6)*R_1,6(12)

Right (Left, Full) Mult Group Orders: 1296 (1296, 5184)

/ revised November, 2001

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	21	23	22	20	18
2	5	4	1	0	3	11	10	7	6	8	9	17	16	13	12	14	15	21	22	18	20	23	19
3	0	1	4	5	2	8	6	9	10	11	7	14	12	15	16	17	13	23	18	22	19	21	20
4	3	0	5	2	1	9	8	10	11	7	6	15	14	16	17	13	12	20	23	21	18	19	22
5	4	3	2	1	0	10	9	11	7	6	8	16	15	17	13	12	14	22	20	19	23	18	21
6	8	9	7	11	10	0	3	1	2	5	4	18	23	19	21	22	20	12	14	17	15	16	13
7	6	8	11	10	9	1	0	2	5	4	3	23	20	18	19	21	22	14	15	13	16	17	12
8	9	10	6	7	11	3	4	0	1	2	5	19	18	21	22	20	23	13	12	16	14	15	17
9	10	11	8	6	7	4	5	3	0	1	2	21	19	22	20	23	18	17	13	15	12	14	16
10	11	7	9	8	6	5	2	4	3	0	1	22	21	20	23	18	19	16	17	14	13	12	15
11	7	6	10	9	8	2	1	5	4	3	0	20	22	23	18	19	21	15	16	12	17	13	14
12	14	15	13	17	16	18	23	19	21	22	20	0	3	1	2	5	4	6	8	11	9	10	7
13	12	14	17	16	15	23	20	18	19	21	22	1	0	2	5	4	3	8	9	7	10	11	6
14	15	16	12	13	17	19	18	21	22	20	23	3	4	0	1	2	5	7	6	10	8	9	11
15	16	17	14	12	13	21	19	22	20	23	18	4	5	3	0	1	2	11	7	9	6	8	10
16	17	13	15	14	12	22	21	20	23	18	19	5	2	4	3	0	1	10	11	8	7	6	9
17	13	12	16	15	14	20	22	23	18	19	21	2	1	5	4	3	0	9	10	6	11	7	8
18	23	20	19	21	22	12	14	13	17	16	15	6	8	7	11	10	9	0	3	2	4	5	1
19	18	23	21	22	20	14	15	12	13	17	16	8	9	6	7	11	10	1	0	5	3	4	2
20	22	21	23	18	19	17	13	16	15	14	12	11	7	10	9	8	6	4	5	0	2	1	3
21	19	18	22	20	23	15	16	14	12	13	17	9	10	8	6	7	11	2	1	4	0	3	5
22	21	19	20	23	18	16	17	15	14	12	13	10	11	9	8	6	7	5	2	3	1	0	4
23	20	22	18	19	21	13	12	17	16	15	14	7	6	11	10	9	8	3	4	1	5	2	0

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	21	23	22	20	18
2	5	4	1	0	3	11	10	7	6	8	9	17	16	13	12	14	15	21	22	18	20	23	19
3	0	1	4	5	2	8	6	9	10	11	7	14	12	15	16	17	13	23	18	22	19	21	20
4	3	0	5	2	1	9	8	10	11	7	6	15	14	16	17	13	12	20	23	21	18	19	22
5	4	3	2	1	0	10	9	11	7	6	8	16	15	17	13	12	14	22	20	19	23	18	21
6	8	9	7	11	10	0	3	1	2	5	4	18	23	19	21	22	20	12	14	17	15	16	13
7	6	8	11	10	9	1	0	2	5	4	3	23	20	18	19	21	22	14	15	13	16	17	12
8	9	10	6	7	11	3	4	0	1	2	5	19	18	21	22	20	23	13	12	16	14	15	17
9	10	11	8	6	7	4	5	3	0	1	2	21	19	22	20	23	18	17	13	15	12	14	16
10	11	7	9	8	6	5	2	4	3	0	1	22	21	20	23	18	19	16	17	14	13	12	15
11	7	6	10	9	8	2	1	5	4	3	0	20	22	23	18	19	21	15	16	12	17	13	14
12	14	15	13	17	16	18	23	19	21	22	20	0	3	1	2	5	4	6	8	11	9	10	7
13	12	14	17	16	15	23	20	18	19	21	22	1	0	2	5	4	3	8	9	7	10	11	6
14	15	16	12	13	17	19	18	21	22	20	23	3	4	0	1	2	5	7	6	10	8	9	11
15	16	17	14	12	13	21	19	22	20	23	18	4	5	3	0	1	2	11	7	9	6	8	10
16	17	13	15	14	12	22	21	20	23	18	19	5	2	4	3	0	1	10	11	8	7	6	9
17	13	12	16	15	14	20	22	23	18	19	21	2	1	5	4	3	0	9	10	6	11	7	8
18	23	20	19	21	22	12	14	13	17	16	15	6	8	7	11	10	9	0	3	2	4	5	1
19	18	23	21	22	20	14	15	12	13	17	16	8	9	6	7	11	10	1	0	5	3	4	2
20	22	21	23	18	19	17	13	16	15	14	12	11	7	10	9	8	6	4	5	0	2	1	3
21	19	18	22	20	23	15	16	14	12	13	17	9	10	8	6	7	11	2	1	4	0	3	5
22	21	19	20	23	18	16	17	15	14	12	13	10	11	9	8	6	7	5	2	3	1	0	4
23	20	22	18	19	21	13	12	17	16	15	14	7	6	11	10	9	8	3	4	1	5	2	0

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	21	23	22	20	18
2	5	4	1	0	3	11	10	7	6	8	9	17	16	13	12	14	15	21	22	18	20	23	19
3	0	1	4	5	2	8	6	9	10	11	7	14	12	15	16	17	13	23	18	22	19	21	20
4	3	0	5	2	1	9	8	10	11	7	6	15	14	16	17	13	12	20	23	21	18	19	22
5	4	3	2	1	0	10	9	11	7	6	8	16	15	17	13	12	14	22	20	19	23	18	21
6	8	9	7	11	10	0	3	1	2	5	4	18	23	19	21	22	20	12	14	17	15	16	13
7	6	8	11	10	9	1	0	2	5	4	3	23	20	18	19	21	22	14	15	13	16	17	12
8	9	10	6	7	11	3	4	0	1	2	5	19	18	21	22	20	23	13	12	16	14	15	17
9	10	11	8	6	7	4	5	3	0	1	2	21	19	22	20	23	18	17	13	15	12	14	16
10	11	7	9	8	6	5	2	4	3	0	1	22	21	20	23	18	19	16	17	14	13	12	15
11	7	6	10	9	8	2	1	5	4	3	0	20	22	23	18	19	21	15	16	12	17	13	14
12	14	15	13	17	16	18	23	19	21	22	20	0	3	1	2	5	4	6	8	11	9	10	7
13	12	14	17	16	15	23	20	18	19	21	22	1	0	2	5	4	3	8	9	7	10	11	6
14	15	16	12	13	17	19	18	21	22	20	23	3	4	0	1	2	5	7	6	10	8	9	11
15	16	17	14	12	13	21	19	22	20	23	18	4	5	3	0	1	2	11	7	9	6	8	10
16	17	13	15	14	12	22	21	20	23	18	19	5	2	4	3	0	1	10	11	8	7	6	9
17	13	12	16	15	14	20	22	23	18	19	21	2	1	5	4	3	0	9	10	6	11	7	8
18	23	20	19	21	22	12	14	13	17	16	15	6	8	7	11	10	9	0	3	2	4	5	1
19	18	23	21	22	20	14	15	12	13	17	16	8	9	6	7	11	10	1	0	5	3	4	2
20	22	21	23	18	19	17	13	16	15	14	12	11	7	10	9	8	6	4	5	0	2	1	3
21	19	18	22	20	23	15	16	14	12	13	17	9	10	8	6	7	11	2	1	4	0	3	5
22	21	19	20	23	18	16	17	15	14	12	13	10	11	9	8	6	7	5	2	3	1	0	4
23	20	22	18	19	21	13	12	17	16	15	14	7	6	11	10	9	8	3	4	1	5	2	0