Moufang Loop 24.13.2.6 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	3	0	5	9	10	4	11	7	8	6	13	15	12	14	19	22	16	21	23	18	20	17
2	3	0	1	9	7	8	5	6	4	11	10	15	14	13	12	21	20	19	18	17	16	23	22
3	0	1	2	7	4	11	9	10	5	6	8	14	12	15	13	18	23	21	16	22	19	17	20
4	6	9	8	10	1	7	3	5	11	2	0	16	22	23	21	20	12	14	13	15	17	18	19
5	10	7	11	8	2	4	0	9	6	3	1	22	21	16	23	13	18	20	17	19	14	15	12
6	9	8	4	1	11	2	10	0	3	5	7	19	20	17	18	23	13	12	15	14	22	16	21
7	11	5	10	6	0	9	2	4	8	1	3	23	16	21	22	14	19	17	20	18	13	12	15
8	4	6	9	3	10	0	11	2	1	7	5	18	17	20	19	22	14	15	12	13	23	21	16
9	8	4	6	11	3	5	1	7	10	0	2	21	23	22	16	17	15	13	14	12	20	19	18
10	7	11	5	2	6	3	8	1	0	9	4	20	18	19	17	15	16	23	22	21	12	14	13
11	5	10	7	0	8	1	6	3	2	4	9	17	19	18	20	12	21	22	23	16	15	13	14
12	14	15	13	17	23	18	22	19	20	21	16	0	3	1	2	11	4	6	8	9	10	7	5
13	12	14	15	19	16	17	21	20	18	23	22	1	0	2	3	5	6	9	4	8	7	11	10
14	15	13	12	18	21	20	16	17	19	22	23	3	2	0	1	7	8	4	9	6	5	10	11
15	13	12	14	20	22	19	23	18	17	16	21	2	1	3	0	10	9	8	6	4	11	5	7
16	18	21	19	12	14	22	13	23	15	17	20	4	7	5	9	0	10	1	3	11	2	6	8
17	23	20	22	21	19	14	18	13	16	15	12	11	8	6	10	9	0	7	5	2	4	3	1
18	21	19	16	22	17	15	20	12	23	13	14	8	10	11	6	3	5	0	2	7	1	4	9
19	16	18	21	23	20	12	17	15	22	14	13	6	11	10	8	1	7	2	0	5	3	9	4
20	22	17	23	16	18	13	19	14	21	12	15	10	6	8	11	4	2	5	7	0	9	1	3
21	19	16	18	15	13	23	14	22	12	20	17	9	5	7	4	2	11	3	1	10	0	8	6
22	17	23	20	13	12	21	15	16	14	19	18	5	4	9	7	8	1	11	10	3	6	0	2
23	20	22	17	14	15	16	12	21	13	18	19	7	9	4	5	6	3	10	11	1	8	2	0

Centre: 0 2

Centrum: 0 2

Nucleus: 0 2

Left Nucleus: 0 2

Middle Nucleus: 0 2

Right Nucleus: 0 2

1 Element of order 1: 0

13 Elements of order 2: 2 12 13 14 15 16 17 18 19 20 21 22 23

2 Elements of order 3: 9 10

6 Elements of order 4: 1 3 5 6 7 8

2 Elements of order 6: 4 11

Commutator Subloop: 0 2 4 9 10 11

Associator Subloop: 0 9 10

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

4 11
9 10

3 Conjugacy Classes of size 6:

1 3 5 6 7 8
12 15 16 17 20 21
13 14 18 19 22 23

Automorphic Inverse Property: FAILS. (1^-1)(5^-1) neq (1*5)^-1

A_l Property: FAILS. The left inner mapping L_1,4 = (12,21,20)(13,23,18)(14,22,19)(15,16,17) is not an automorphism. L_1,4(1*12) neq L_1,4(1)*L_1,4(12)

A_r Property: FAILS. The right inner mapping R_1,4 = (12,20,21)(13,18,23)(14,19,22)(15,17,16) is not an automorphism. R_1,4(1*12) neq R_1,4(1)*R_1,4(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	3	0	5	9	10	4	11	7	8	6	13	15	12	14	19	22	16	21	23	18	20	17
2	3	0	1	9	7	8	5	6	4	11	10	15	14	13	12	21	20	19	18	17	16	23	22
3	0	1	2	7	4	11	9	10	5	6	8	14	12	15	13	18	23	21	16	22	19	17	20
4	6	9	8	10	1	7	3	5	11	2	0	16	22	23	21	20	12	14	13	15	17	18	19
5	10	7	11	8	2	4	0	9	6	3	1	22	21	16	23	13	18	20	17	19	14	15	12
6	9	8	4	1	11	2	10	0	3	5	7	19	20	17	18	23	13	12	15	14	22	16	21
7	11	5	10	6	0	9	2	4	8	1	3	23	16	21	22	14	19	17	20	18	13	12	15
8	4	6	9	3	10	0	11	2	1	7	5	18	17	20	19	22	14	15	12	13	23	21	16
9	8	4	6	11	3	5	1	7	10	0	2	21	23	22	16	17	15	13	14	12	20	19	18
10	7	11	5	2	6	3	8	1	0	9	4	20	18	19	17	15	16	23	22	21	12	14	13
11	5	10	7	0	8	1	6	3	2	4	9	17	19	18	20	12	21	22	23	16	15	13	14
12	14	15	13	17	23	18	22	19	20	21	16	0	3	1	2	11	4	6	8	9	10	7	5
13	12	14	15	19	16	17	21	20	18	23	22	1	0	2	3	5	6	9	4	8	7	11	10
14	15	13	12	18	21	20	16	17	19	22	23	3	2	0	1	7	8	4	9	6	5	10	11
15	13	12	14	20	22	19	23	18	17	16	21	2	1	3	0	10	9	8	6	4	11	5	7
16	18	21	19	12	14	22	13	23	15	17	20	4	7	5	9	0	10	1	3	11	2	6	8
17	23	20	22	21	19	14	18	13	16	15	12	11	8	6	10	9	0	7	5	2	4	3	1
18	21	19	16	22	17	15	20	12	23	13	14	8	10	11	6	3	5	0	2	7	1	4	9
19	16	18	21	23	20	12	17	15	22	14	13	6	11	10	8	1	7	2	0	5	3	9	4
20	22	17	23	16	18	13	19	14	21	12	15	10	6	8	11	4	2	5	7	0	9	1	3
21	19	16	18	15	13	23	14	22	12	20	17	9	5	7	4	2	11	3	1	10	0	8	6
22	17	23	20	13	12	21	15	16	14	19	18	5	4	9	7	8	1	11	10	3	6	0	2
23	20	22	17	14	15	16	12	21	13	18	19	7	9	4	5	6	3	10	11	1	8	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	3	0	5	9	10	4	11	7	8	6	13	15	12	14	19	22	16	21	23	18	20	17
2	3	0	1	9	7	8	5	6	4	11	10	15	14	13	12	21	20	19	18	17	16	23	22
3	0	1	2	7	4	11	9	10	5	6	8	14	12	15	13	18	23	21	16	22	19	17	20
4	6	9	8	10	1	7	3	5	11	2	0	16	22	23	21	20	12	14	13	15	17	18	19
5	10	7	11	8	2	4	0	9	6	3	1	22	21	16	23	13	18	20	17	19	14	15	12
6	9	8	4	1	11	2	10	0	3	5	7	19	20	17	18	23	13	12	15	14	22	16	21
7	11	5	10	6	0	9	2	4	8	1	3	23	16	21	22	14	19	17	20	18	13	12	15
8	4	6	9	3	10	0	11	2	1	7	5	18	17	20	19	22	14	15	12	13	23	21	16
9	8	4	6	11	3	5	1	7	10	0	2	21	23	22	16	17	15	13	14	12	20	19	18
10	7	11	5	2	6	3	8	1	0	9	4	20	18	19	17	15	16	23	22	21	12	14	13
11	5	10	7	0	8	1	6	3	2	4	9	17	19	18	20	12	21	22	23	16	15	13	14
12	14	15	13	17	23	18	22	19	20	21	16	0	3	1	2	11	4	6	8	9	10	7	5
13	12	14	15	19	16	17	21	20	18	23	22	1	0	2	3	5	6	9	4	8	7	11	10
14	15	13	12	18	21	20	16	17	19	22	23	3	2	0	1	7	8	4	9	6	5	10	11
15	13	12	14	20	22	19	23	18	17	16	21	2	1	3	0	10	9	8	6	4	11	5	7
16	18	21	19	12	14	22	13	23	15	17	20	4	7	5	9	0	10	1	3	11	2	6	8
17	23	20	22	21	19	14	18	13	16	15	12	11	8	6	10	9	0	7	5	2	4	3	1
18	21	19	16	22	17	15	20	12	23	13	14	8	10	11	6	3	5	0	2	7	1	4	9
19	16	18	21	23	20	12	17	15	22	14	13	6	11	10	8	1	7	2	0	5	3	9	4
20	22	17	23	16	18	13	19	14	21	12	15	10	6	8	11	4	2	5	7	0	9	1	3
21	19	16	18	15	13	23	14	22	12	20	17	9	5	7	4	2	11	3	1	10	0	8	6
22	17	23	20	13	12	21	15	16	14	19	18	5	4	9	7	8	1	11	10	3	6	0	2
23	20	22	17	14	15	16	12	21	13	18	19	7	9	4	5	6	3	10	11	1	8	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	3	0	5	9	10	4	11	7	8	6	13	15	12	14	19	22	16	21	23	18	20	17
2	3	0	1	9	7	8	5	6	4	11	10	15	14	13	12	21	20	19	18	17	16	23	22
3	0	1	2	7	4	11	9	10	5	6	8	14	12	15	13	18	23	21	16	22	19	17	20
4	6	9	8	10	1	7	3	5	11	2	0	16	22	23	21	20	12	14	13	15	17	18	19
5	10	7	11	8	2	4	0	9	6	3	1	22	21	16	23	13	18	20	17	19	14	15	12
6	9	8	4	1	11	2	10	0	3	5	7	19	20	17	18	23	13	12	15	14	22	16	21
7	11	5	10	6	0	9	2	4	8	1	3	23	16	21	22	14	19	17	20	18	13	12	15
8	4	6	9	3	10	0	11	2	1	7	5	18	17	20	19	22	14	15	12	13	23	21	16
9	8	4	6	11	3	5	1	7	10	0	2	21	23	22	16	17	15	13	14	12	20	19	18
10	7	11	5	2	6	3	8	1	0	9	4	20	18	19	17	15	16	23	22	21	12	14	13
11	5	10	7	0	8	1	6	3	2	4	9	17	19	18	20	12	21	22	23	16	15	13	14
12	14	15	13	17	23	18	22	19	20	21	16	0	3	1	2	11	4	6	8	9	10	7	5
13	12	14	15	19	16	17	21	20	18	23	22	1	0	2	3	5	6	9	4	8	7	11	10
14	15	13	12	18	21	20	16	17	19	22	23	3	2	0	1	7	8	4	9	6	5	10	11
15	13	12	14	20	22	19	23	18	17	16	21	2	1	3	0	10	9	8	6	4	11	5	7
16	18	21	19	12	14	22	13	23	15	17	20	4	7	5	9	0	10	1	3	11	2	6	8
17	23	20	22	21	19	14	18	13	16	15	12	11	8	6	10	9	0	7	5	2	4	3	1
18	21	19	16	22	17	15	20	12	23	13	14	8	10	11	6	3	5	0	2	7	1	4	9
19	16	18	21	23	20	12	17	15	22	14	13	6	11	10	8	1	7	2	0	5	3	9	4
20	22	17	23	16	18	13	19	14	21	12	15	10	6	8	11	4	2	5	7	0	9	1	3
21	19	16	18	15	13	23	14	22	12	20	17	9	5	7	4	2	11	3	1	10	0	8	6
22	17	23	20	13	12	21	15	16	14	19	18	5	4	9	7	8	1	11	10	3	6	0	2
23	20	22	17	14	15	16	12	21	13	18	19	7	9	4	5	6	3	10	11	1	8	2	0