Right Bol Loop 24.11.2.0 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	2	5	0	3	4	11	10	9	6	8	7	13	12	15	14	17	16	21	23	22	18	20	19
2	5	4	1	0	3	7	8	6	11	9	10	17	14	16	12	13	15	19	20	18	22	23	21
3	0	1	4	5	2	9	11	10	8	7	6	14	17	12	16	15	13	22	21	23	19	18	20
4	3	0	5	2	1	8	6	7	10	11	9	15	16	13	17	14	12	20	18	19	23	21	22
5	4	3	2	1	0	10	9	11	7	6	8	16	15	17	13	12	14	23	22	21	20	19	18
6	11	7	9	8	10	0	2	4	3	5	1	20	23	22	18	21	19	15	17	12	16	14	13
7	10	8	11	6	9	2	4	0	1	3	5	19	22	21	20	23	18	17	12	15	14	13	16
8	9	6	10	7	11	4	0	2	5	1	3	18	21	23	19	22	20	12	15	17	13	16	14
9	6	11	8	10	7	3	1	5	4	2	0	22	19	20	21	18	23	14	16	13	17	15	12
10	8	9	7	11	6	5	3	1	2	0	4	21	18	19	23	20	22	13	14	16	12	17	15
11	7	10	6	9	8	1	5	3	0	4	2	23	20	18	22	19	21	16	13	14	15	12	17
12	18	17	19	15	20	16	14	13	22	21	23	0	1	3	4	5	2	8	7	6	10	9	11
13	22	16	21	14	23	15	12	17	20	18	19	1	0	4	3	2	5	10	11	9	8	6	7
14	21	13	23	16	22	17	15	12	18	19	20	3	2	0	5	4	1	9	10	11	7	8	6
15	19	12	20	17	18	13	16	14	21	23	22	4	5	1	2	3	0	6	8	7	11	10	9
16	23	14	22	13	21	12	17	15	19	20	18	5	4	2	1	0	3	11	9	10	6	7	8
17	20	15	18	12	19	14	13	16	23	22	21	2	3	5	0	1	4	7	6	8	9	11	10
18	17	20	12	19	15	23	21	22	16	13	14	8	10	11	7	9	6	0	4	2	1	5	3
19	12	18	15	20	17	22	23	21	13	14	16	7	9	10	6	11	8	2	0	4	3	1	5
20	15	19	17	18	12	21	22	23	14	16	13	6	11	9	8	10	7	4	2	0	5	3	1
21	13	22	14	23	16	20	19	18	17	12	15	10	8	7	11	6	9	1	3	5	0	2	4
22	16	23	13	21	14	19	18	20	15	17	12	9	7	6	10	8	11	3	5	1	2	4	0
23	14	21	16	22	13	18	20	19	12	15	17	11	6	8	9	7	10	5	1	3	4	0	2

Centre: 0 10

Centrum: 0 10

Nucleus: 0 10

Left Nucleus: 0 5 6 10

Middle Nucleus: 0 2 4 9 10 11

Right Nucleus: 0 2 4 9 10 11

1 Element of order 1: 0

11 Elements of order 2: 5 6 10 12 13 14 16 18 19 20 21

2 Elements of order 3: 2 4

10 Elements of order 6: 1 3 7 8 9 11 15 17 22 23

Commutator Subloop: 0 2 4 9 10 11

Associator Subloop: 0 2 4 9 10 11

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

2 4
9 11

3 Conjugacy Classes of size 6:

1 3 5 6 7 8
12 15 17 21 22 23
13 14 16 18 19 20

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

A_l Property: FAILS. The left inner mapping L_1,1 = (12,15,17)(13,16,14)(18,20,19)(21,23,22) is not an automorphism. L_1,1(1*12) neq L_1,1(1)*L_1,1(12)

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

Right (Left, Full) Mult Group Orders: 48 (2592, 10368)

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