Moufang Loop 24.15.1.0 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	0	4	6	8	3	10	9	5	11	7	13	14	12	19	20	15	23	17	22	18	16	21
2	0	1	6	3	9	4	11	5	8	7	10	14	12	13	17	22	19	21	15	16	23	20	18
3	5	7	8	2	10	11	4	0	6	1	9	15	22	21	16	12	23	13	14	17	19	18	20
4	8	10	9	0	11	7	6	1	3	2	5	22	21	15	14	17	16	20	23	18	13	12	19
5	7	3	2	11	0	8	1	6	10	9	4	19	16	18	20	13	21	14	12	15	17	23	22
6	9	11	5	1	7	10	3	2	4	0	8	21	15	22	23	18	14	19	16	12	20	17	13
7	3	5	11	8	6	2	9	10	0	4	1	17	20	23	22	14	18	12	13	19	15	21	16
8	10	4	0	7	1	9	2	3	11	5	6	16	18	19	12	15	20	22	21	23	14	13	17
9	11	6	1	10	2	5	0	4	7	8	3	18	19	16	21	23	12	17	20	13	22	15	14
10	4	8	7	9	3	0	5	11	1	6	2	20	23	17	13	19	22	16	18	21	12	14	15
11	6	9	10	5	4	1	8	7	2	3	0	23	17	20	18	21	13	15	22	14	16	19	12
12	14	13	16	22	19	20	18	15	17	21	23	0	2	1	8	3	9	7	5	6	10	4	11
13	12	14	18	21	16	23	19	22	20	15	17	1	0	2	10	5	11	3	7	9	4	8	6
14	13	12	19	15	18	17	16	21	23	22	20	2	1	0	4	7	6	5	3	11	8	10	9
15	17	19	12	14	20	13	21	16	22	23	18	3	6	4	0	8	1	11	2	5	7	9	10
16	22	20	15	17	13	19	23	12	14	18	21	8	5	9	3	0	4	10	6	2	11	1	7
17	19	15	20	16	21	22	12	23	18	14	13	7	11	10	2	4	0	9	1	3	5	6	8
18	21	23	22	20	14	16	17	13	12	19	15	9	8	5	11	6	7	0	10	4	1	3	2
19	15	17	21	23	12	18	20	14	13	16	22	5	9	8	1	10	2	6	0	7	3	11	4
20	16	22	23	18	15	21	13	17	19	12	14	10	7	11	5	1	8	4	9	0	6	2	3
21	23	18	14	13	17	12	22	19	15	20	16	6	4	3	9	11	5	2	8	10	0	7	1
22	20	16	13	12	23	14	15	18	21	17	19	4	3	6	7	2	10	8	11	1	9	0	5
23	18	21	17	19	22	15	14	20	16	13	12	11	10	7	6	9	3	1	4	8	2	5	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: 4 5 11 12 13 14 15 16 17 18 19 20 21 22 23

8 Elements of order 3: 1 2 3 6 7 8 9 10

Commutator Subloop: 0 1 2 3 4 5 6 7 8 9 10 11

Associator Subloop: 0 4 5 11

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 3:

4 5 11

1 Conjugacy Class of size 8:

1 2 3 6 7 8 9 10

1 Conjugacy Class of size 12:

12 13 14 15 16 17 18 19 20 21 22 23

Automorphic Inverse Property: FAILS. (1^-1)(4^-1) neq (1*4)^-1

A_l Property: FAILS. The left inner mapping L_1,3 = (12,23)(13,17)(14,20)(15,18)(16,21)(19,22) is not an automorphism. L_1,3(1*12) neq L_1,3(1)*L_1,3(12)

A_r Property: FAILS. The right inner mapping R_1,3 = (12,23)(13,17)(14,20)(15,18)(16,21)(19,22) is not an automorphism. R_1,3(1*12) neq R_1,3(1)*R_1,3(12)

Right (Left, Full) Mult Group Orders: 4608 (4608, 27648)

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