Moufang Loop 24.7.2.11 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	7	4	6	9	11	8	10	17	18	19	16	12	15	14	13	23	22	20	21
2	3	0	1	7	6	5	4	11	10	9	8	15	14	13	12	17	16	19	18	21	20	23	22
3	0	1	2	6	4	7	5	10	8	11	9	16	19	18	17	15	12	13	14	22	23	21	20
4	5	7	6	2	3	1	0	12	17	16	15	11	20	21	8	9	10	23	22	14	13	18	19
5	7	6	4	3	0	2	1	14	19	18	13	21	11	8	20	23	22	10	9	15	12	17	16
6	4	5	7	1	2	0	3	13	18	19	14	20	8	11	21	22	23	9	10	12	15	16	17
7	6	4	5	0	1	3	2	15	16	17	12	8	21	20	11	10	9	22	23	13	14	19	18
8	9	11	10	12	17	16	15	0	1	3	2	4	22	23	7	6	5	20	21	18	19	13	14
9	11	10	8	14	19	18	13	1	2	0	3	23	4	7	22	20	21	5	6	17	16	12	15
10	8	9	11	13	18	19	14	3	0	2	1	22	7	4	23	21	20	6	5	16	17	15	12
11	10	8	9	15	16	17	12	2	3	1	0	7	23	22	4	5	6	21	20	19	18	14	13
12	14	15	13	11	21	20	8	4	23	22	7	2	1	3	0	18	19	17	16	5	6	9	10
13	12	14	15	9	23	22	10	6	20	21	5	18	16	17	19	0	2	1	3	4	7	8	11
14	15	13	12	10	22	23	9	5	21	20	6	19	17	16	18	2	0	3	1	7	4	11	8
15	13	12	14	8	20	21	11	7	22	23	4	0	3	1	2	19	18	16	17	6	5	10	9
16	18	17	19	20	11	8	21	22	4	7	23	1	0	2	3	13	14	12	15	9	10	6	5
17	19	16	18	21	8	11	20	23	7	4	22	3	2	0	1	14	13	15	12	10	9	5	6
18	17	19	16	23	10	9	22	20	5	6	21	14	12	15	13	1	3	2	0	11	8	4	7
19	16	18	17	22	9	10	23	21	6	5	20	13	15	12	14	3	1	0	2	8	11	7	4
20	23	21	22	17	15	12	16	18	14	13	19	5	9	10	6	4	7	11	8	2	0	1	3
21	22	20	23	16	12	15	17	19	13	14	18	6	10	9	5	7	4	8	11	0	2	3	1
22	20	23	21	18	14	13	19	16	12	15	17	9	6	5	10	8	11	4	7	1	3	0	2
23	21	22	20	19	13	14	18	17	15	12	16	10	5	6	9	11	8	7	4	3	1	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

7 Elements of order 2: 2 5 6 8 11 22 23

2 Elements of order 3: 13 16

12 Elements of order 4: 1 3 4 7 9 10 12 15 18 19 20 21

2 Elements of order 6: 14 17

Commutator Subloop: 0 13 16

Associator Subloop: 0 13 16

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

13 16
14 17

6 Conjugacy Classes of size 3:

1 12 18
3 15 19
4 9 20
5 11 23
6 8 22
7 10 21

Automorphic Inverse Property: FAILS. (1^-1)(13^-1) neq (1*13)^-1

A_l Property: FAILS. The left inner mapping L_1,12 = (4,9,20)(5,23,11)(6,22,8)(7,10,21) is not an automorphism. L_1,12(1*4) neq L_1,12(1)*L_1,12(4)

A_r Property: FAILS. The right inner mapping R_1,12 = (4,9,20)(5,23,11)(6,22,8)(7,10,21) is not an automorphism. R_1,12(1*4) neq R_1,12(1)*R_1,12(4)

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