Right Bol Loop 24.21.1.1 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	14	15	23	17	19	21	16	20	22	18	6	8	7	9	12	2	11	4	10	3	5
2	13	0	15	14	18	16	21	19	17	22	20	23	9	7	8	6	5	1	10	3	11	4	12
3	14	15	0	13	20	21	16	17	19	23	18	22	8	6	9	7	11	4	12	2	5	1	10
4	15	14	13	0	22	19	17	16	21	18	23	20	7	9	6	8	10	3	5	1	12	2	11
5	16	17	19	21	0	18	20	22	23	14	15	13	12	11	10	1	2	6	4	8	3	7	9
6	18	23	22	20	17	0	15	14	13	21	19	16	1	3	4	12	9	5	7	10	8	11	2
7	20	22	23	18	19	15	0	13	14	16	17	21	4	2	1	10	8	11	6	12	9	5	3
8	22	20	18	23	21	14	13	0	15	17	16	19	3	1	2	11	7	10	9	5	6	12	4
9	23	18	20	22	16	13	14	15	0	19	21	17	2	4	3	5	6	12	8	11	7	10	1
10	19	21	16	17	14	22	23	18	20	0	13	15	11	12	5	3	4	8	2	6	1	9	7
11	21	19	17	16	15	20	18	23	22	13	0	14	10	5	12	4	3	7	1	9	2	6	8
12	17	16	21	19	13	23	22	20	18	15	14	0	5	10	11	2	1	9	3	7	4	8	6
13	2	1	4	3	12	9	8	7	6	11	10	5	0	15	14	17	16	23	21	22	19	20	18
14	3	4	1	2	10	8	9	6	7	5	12	11	15	0	13	19	21	22	16	23	17	18	20
15	4	3	2	1	11	7	6	9	8	12	5	10	14	13	0	21	19	20	17	18	16	23	22
16	5	12	10	11	9	2	3	4	1	7	8	6	18	20	22	23	13	17	14	19	15	21	0
17	12	5	11	10	6	1	4	3	2	8	7	9	23	22	20	18	0	16	15	21	14	19	13
18	6	9	8	7	2	5	11	10	12	4	3	1	16	21	19	13	23	0	22	15	20	14	17
19	10	11	5	12	7	4	1	2	3	9	6	8	22	23	18	20	15	21	0	16	13	17	14
20	7	8	9	6	3	11	5	12	10	1	2	4	21	16	17	14	22	15	23	0	18	13	19
21	11	10	12	5	8	3	2	1	4	6	9	7	20	18	23	22	14	19	13	17	0	16	15
22	8	7	6	9	4	10	12	5	11	2	1	3	19	17	16	15	20	14	18	13	23	0	21
23	9	6	7	8	1	12	10	11	5	3	4	2	17	19	21	0	18	13	20	14	22	15	16

Centre: 0

Centrum: 0

Nucleus: 0

Left Nucleus: 0 13 14 15

Middle Nucleus: 0 16 23

Right Nucleus: 0 16 23

1 Element of order 1: 0

21 Elements of order 2: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22

2 Elements of order 3: 16 23

Commutator Subloop: 0 13 16 17 18 23

Associator Subloop: 0 13 16 17 18 23

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 2:

16 23

1 Conjugacy Class of size 3:

13 17 18

3 Conjugacy Classes of size 6:

1 2 5 6 9 12
3 4 7 8 10 11
14 15 19 20 21 22

Automorphic Inverse Property: FAILS. (1^-1)(6^-1) neq (1*6)^-1

A_l Property: FAILS. The left inner mapping L_1,1 = (2,6,12)(3,8,10,4,7,11)(13,17,18)(14,21,20,15,19,22) 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, 839808)

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

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

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