Right Bol Loop 24.7.2.3 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	11	4	10	7	6	8	18	19	17	16	14	15	13	12	22	23	21	20
2	3	0	1	9	7	8	5	6	4	11	10	13	12	15	14	17	16	19	18	21	20	23	22
3	0	1	2	7	4	10	9	11	5	8	6	19	18	16	17	15	14	12	13	23	22	20	21
4	6	9	8	2	3	12	1	13	0	19	18	23	22	7	5	21	20	10	11	16	17	14	15
5	11	7	10	3	0	18	2	19	1	12	13	20	21	4	9	23	22	6	8	14	15	17	16
6	9	8	4	14	17	0	16	2	15	3	1	10	11	20	21	7	5	22	23	12	13	18	19
7	10	5	11	1	2	19	0	18	3	13	12	21	20	9	4	22	23	8	6	15	14	16	17
8	4	6	9	15	16	2	17	0	14	1	3	11	10	21	20	5	7	23	22	13	12	19	18
9	8	4	6	0	1	13	3	12	2	18	19	22	23	5	7	20	21	11	10	17	16	15	14
10	5	11	7	16	14	3	15	1	17	2	0	8	6	23	22	9	4	20	21	19	18	12	13
11	7	10	5	17	15	1	14	3	16	0	2	6	8	22	23	4	9	21	20	18	19	13	12
12	17	13	16	23	20	4	21	9	22	7	5	2	0	19	18	1	3	14	15	8	6	10	11
13	16	12	17	22	21	9	20	4	23	5	7	0	2	18	19	3	1	15	14	6	8	11	10
14	18	15	19	8	10	20	11	21	6	23	22	16	17	2	0	13	12	3	1	7	5	4	9
15	19	14	18	6	11	21	10	20	8	22	23	17	16	0	2	12	13	1	3	5	7	9	4
16	12	17	13	11	8	23	6	22	10	21	20	15	14	1	3	18	19	2	0	9	4	7	5
17	13	16	12	10	6	22	8	23	11	20	21	14	15	3	1	19	18	0	2	4	9	5	7
18	15	19	14	20	22	5	23	7	21	4	9	3	1	12	13	2	0	17	16	10	11	6	8
19	14	18	15	21	23	7	22	5	20	9	4	1	3	13	12	0	2	16	17	11	10	8	6
20	22	21	23	19	12	14	13	15	18	16	17	7	5	8	6	11	10	4	9	2	0	3	1
21	23	20	22	18	13	15	12	14	19	17	16	5	7	6	8	10	11	9	4	0	2	1	3
22	21	23	20	12	18	17	19	16	13	14	15	4	9	10	11	8	6	5	7	3	1	0	2
23	20	22	21	13	19	16	18	17	12	15	14	9	4	11	10	6	8	7	5	1	3	2	0

Centre: 0 2

Centrum: 0 2

Nucleus: 0 2

Left Nucleus: 0 1 2 3 20 21 22 23

Middle Nucleus: 0 2 16 17 18 19

Right Nucleus: 0 2 16 17 18 19

1 Element of order 1: 0

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

2 Elements of order 3: 17 18

12 Elements of order 4: 1 3 4 9 10 11 12 13 14 15 20 21

2 Elements of order 6: 16 19

Commutator Subloop: 0 17 18

Associator Subloop: 0 17 18

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

16 19
17 18

6 Conjugacy Classes of size 3:

1 13 15
3 12 14
4 10 20
5 6 22
7 8 23
9 11 21

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

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

A_r Property: HOLDS (i.e. every right inner mapping R_a,b is an automorphism)

Right (Left, Full) Mult Group Orders: 48 (648, 1296)

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