Moufang Loop 24.1.2.9 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	13	18	8	23	11	20	19	22	21	12	14	15	16	17	10
2	3	0	1	7	6	5	4	13	11	12	9	10	8	15	14	17	16	23	20	19	22	21	18
3	0	1	2	6	4	7	5	11	8	23	13	18	9	19	20	21	22	10	15	14	17	16	12
4	6	7	5	2	1	3	0	14	19	17	20	16	15	13	8	10	12	22	11	9	18	23	21
5	4	6	7	3	2	0	1	16	21	14	22	15	17	12	10	13	8	19	23	18	11	9	20
6	7	5	4	1	0	2	3	17	22	15	21	14	16	10	12	8	13	20	18	23	9	11	19
7	5	4	6	0	3	1	2	15	20	16	19	17	14	8	13	12	10	21	9	11	23	18	22
8	10	13	12	15	17	16	14	2	23	3	18	1	0	4	7	5	6	9	22	21	19	20	11
9	18	11	23	17	14	15	16	3	10	0	12	2	1	21	22	20	19	13	4	7	5	6	8
10	13	12	8	19	21	22	20	23	0	9	2	11	18	5	6	7	4	1	17	16	14	15	3
11	23	9	18	16	15	14	17	1	12	2	10	0	3	22	21	19	20	8	7	4	6	5	13
12	8	10	13	20	22	21	19	18	2	11	0	9	23	6	5	4	7	3	16	17	15	14	1
13	12	8	10	14	16	17	15	0	18	1	23	3	2	7	4	6	5	11	21	22	20	19	9
14	19	15	20	8	11	9	13	7	5	21	6	22	4	2	0	18	23	17	3	1	12	10	16
15	20	14	19	13	9	11	8	4	6	22	5	21	7	0	2	23	18	16	1	3	10	12	17
16	21	17	22	9	8	13	11	6	7	20	4	19	5	23	18	2	0	14	10	12	3	1	15
17	22	16	21	11	13	8	9	5	4	19	7	20	6	18	23	0	2	15	12	10	1	3	14
18	11	23	9	21	20	19	22	10	1	13	3	8	12	16	17	15	14	2	5	6	7	4	0
19	15	20	14	12	18	23	10	21	17	4	16	7	22	1	3	9	11	6	2	0	13	8	5
20	14	19	15	10	23	18	12	22	16	7	17	4	21	3	1	11	9	5	0	2	8	13	6
21	17	22	16	23	12	10	18	20	14	5	15	6	19	11	9	1	3	4	8	13	2	0	7
22	16	21	17	18	10	12	23	19	15	6	14	5	20	9	11	3	1	7	13	8	0	2	4
23	9	18	11	22	19	20	21	12	3	8	1	13	10	17	16	14	15	0	6	5	4	7	2

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

1 Element of order 2: 2

2 Elements of order 3: 9 10

18 Elements of order 4: 1 3 4 5 6 7 8 13 14 15 16 17 18 19 20 21 22 23

2 Elements of order 6: 11 12

Commutator Subloop: 0 2 9 10 11 12

Associator Subloop: 0 9 10

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

9 10
11 12

3 Conjugacy Classes of size 6:

1 3 8 13 18 23
4 7 16 17 19 20
5 6 14 15 21 22

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

A_l Property: FAILS. The left inner mapping L_1,8 = (4,19,17)(5,21,14)(6,22,15)(7,20,16) is not an automorphism. L_1,8(1*4) neq L_1,8(1)*L_1,8(4)

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

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

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