Right Bol Loop 24.7.2.0 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	7	11	6	8	9	10	13	17	12	14	15	16	19	20	21	22	23	18
2	5	4	1	0	3	11	10	7	6	8	9	17	16	13	12	14	15	20	21	22	23	18	19
3	0	1	4	5	2	8	6	9	10	11	7	14	12	15	16	17	13	23	18	19	20	21	22
4	3	0	5	2	1	9	8	10	11	7	6	15	14	16	17	13	12	22	23	18	19	20	21
5	4	3	2	1	0	10	9	11	7	6	8	16	15	17	13	12	14	21	22	23	18	19	20
6	8	9	7	11	10	0	3	1	2	5	4	18	19	23	22	21	20	12	13	17	16	15	14
7	6	8	11	10	9	1	0	2	5	4	3	23	18	22	21	20	19	14	12	13	17	16	15
8	9	10	6	7	11	3	4	0	1	2	5	19	20	18	23	22	21	13	17	16	15	14	12
9	10	11	8	6	7	4	5	3	0	1	2	20	21	19	18	23	22	17	16	15	14	12	13
10	11	7	9	8	6	5	2	4	3	0	1	21	22	20	19	18	23	16	15	14	12	13	17
11	7	6	10	9	8	2	1	5	4	3	0	22	23	21	20	19	18	15	14	12	13	17	16
12	13	17	14	15	16	23	22	18	19	20	21	1	2	0	3	4	5	8	9	10	11	7	6
13	17	16	12	14	15	22	21	23	18	19	20	2	5	1	0	3	4	9	10	11	7	6	8
14	12	13	15	16	17	18	23	19	20	21	22	0	1	3	4	5	2	6	8	9	10	11	7
15	14	12	16	17	13	19	18	20	21	22	23	3	0	4	5	2	1	7	6	8	9	10	11
16	15	14	17	13	12	20	19	21	22	23	18	4	3	5	2	1	0	11	7	6	8	9	10
17	16	15	13	12	14	21	20	22	23	18	19	5	4	2	1	0	3	10	11	7	6	8	9
18	19	20	23	22	21	14	15	12	13	17	16	8	9	6	7	11	10	1	2	5	4	3	0
19	20	21	18	23	22	15	16	14	12	13	17	9	10	8	6	7	11	2	5	4	3	0	1
20	21	22	19	18	23	16	17	15	14	12	13	10	11	9	8	6	7	5	4	3	0	1	2
21	22	23	20	19	18	17	13	16	15	14	12	11	7	10	9	8	6	4	3	0	1	2	5
22	23	18	21	20	19	13	12	17	16	15	14	7	6	11	10	9	8	3	0	1	2	5	4
23	18	19	22	21	20	12	14	13	17	16	15	6	8	7	11	10	9	0	1	2	5	4	3

Centre: 0 5

Centrum: 0 5

Nucleus: 0 5

Left Nucleus: 0 5 6 10

Middle Nucleus: 0 1 2 3 4 5

Right Nucleus: 0 1 2 3 4 5

1 Element of order 1: 0

7 Elements of order 2: 5 6 7 8 9 10 11

2 Elements of order 3: 2 4

4 Elements of order 4: 13 15 19 22

2 Elements of order 6: 1 3

8 Elements of order 12: 12 14 16 17 18 20 21 23

Commutator Subloop: 0 1 2 3 4 5

Associator Subloop: 0 1 2 3 4 5

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

3 Conjugacy Classes of size 6:

6 7 8 9 10 11
12 13 14 15 16 17
18 19 20 21 22 23

Automorphic Inverse Property: FAILS. (1^-1)(7^-1) neq (1*7)^-1

A_l Property: FAILS. The left inner mapping L_6,1 = (12,17,15)(13,16,14)(18,20,22)(19,21,23) is not an automorphism. L_6,1(12*6) neq L_6,1(12)*L_6,1(6)

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

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

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