Right Bol Loop 24.13.1.0 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	0	13	17	14	15	16	20	19	18	22	23	21	7	4	8	6	9	2	3	5	11	12	10
2	13	0	14	17	16	15	22	21	23	20	18	19	12	3	11	5	10	6	1	4	8	7	9
3	15	14	16	13	0	17	23	22	21	19	20	18	10	5	12	2	11	1	4	6	9	8	7
4	16	17	15	0	13	14	18	20	19	21	22	23	9	6	7	1	8	3	5	2	10	11	12
5	17	16	0	15	14	13	21	23	22	18	19	20	11	2	10	3	12	4	6	1	7	9	8
6	14	15	13	16	17	0	19	18	20	23	21	22	8	1	9	4	7	5	2	3	12	10	11
7	18	22	23	19	21	20	16	14	0	13	17	15	4	9	1	8	6	12	10	11	5	2	3
8	19	21	22	20	23	18	14	0	16	17	15	13	1	7	6	9	4	11	12	10	2	3	5
9	20	23	21	18	22	19	0	16	14	15	13	17	6	8	4	7	1	10	11	12	3	5	2
10	23	20	18	21	19	22	15	17	13	0	14	16	5	11	3	12	2	7	9	8	4	6	1
11	22	18	19	23	20	21	13	15	17	16	0	14	2	12	5	10	3	9	8	7	1	4	6
12	21	19	20	22	18	23	17	13	15	14	16	0	3	10	2	11	5	8	7	9	6	1	4
13	2	1	4	3	6	5	10	12	11	7	9	8	14	17	0	15	16	21	22	23	18	19	20
14	6	3	5	1	2	4	9	7	8	12	10	11	17	16	13	0	15	19	20	18	23	21	22
15	3	6	1	5	4	2	12	11	10	9	8	7	0	13	16	17	14	23	21	22	19	20	18
16	4	5	2	6	3	1	8	9	7	11	12	10	15	0	17	14	13	20	18	19	22	23	21
17	5	4	6	2	1	3	11	10	12	8	7	9	16	15	14	13	0	22	23	21	20	18	19
18	7	11	12	9	10	8	1	6	4	5	2	3	21	19	23	20	22	16	0	14	13	17	15
19	8	12	10	7	11	9	4	1	6	3	5	2	22	20	21	18	23	0	14	16	15	13	17
20	9	10	11	8	12	7	6	4	1	2	3	5	23	18	22	19	21	14	16	0	17	15	13
21	12	8	7	10	9	11	3	2	5	4	6	1	19	22	18	23	20	15	13	17	0	14	16
22	11	7	9	12	8	10	5	3	2	1	4	6	20	23	19	21	18	13	17	15	16	0	14
23	10	9	8	11	7	12	2	5	3	6	1	4	18	21	20	22	19	17	15	13	14	16	0

Centre: 0

Centrum: 0

Nucleus: 0

Left Nucleus: 0 17 20 21

Middle Nucleus: 0 14 16

Right Nucleus: 0 14 16

1 Element of order 1: 0

13 Elements of order 2: 1 2 4 6 8 10 11 12 17 20 21 22 23

2 Elements of order 3: 14 16

8 Elements of order 6: 3 5 7 9 13 15 18 19

Commutator Subloop: 0 14 16 21 22 23

Associator Subloop: 0 14 16 21 22 23

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 2:

14 16

1 Conjugacy Class of size 3:

21 22 23

3 Conjugacy Classes of size 6:

1 4 6 10 11 12
2 3 5 7 8 9
13 15 17 18 19 20

Automorphic Inverse Property: FAILS. (1^-1)(3^-1) neq (1*3)^-1

A_l Property: FAILS. The left inner mapping L_1,1 = (2,7,5,8,3,9)(10,12,11)(13,20,15,19,17,18)(21,23,22) is not an automorphism. L_1,1(2*1) neq L_1,1(2)*L_1,1(1)

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

Right (Left, Full) Mult Group Orders: 96 (69984, 279936)

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