Right Bol Loop 24.15.4.1 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	2	5	0	3	4	7	6	9	8	11	10	13	12	15	14	17	16	23	18	19	20	21	22
2	5	4	1	0	3	11	8	10	6	7	9	17	14	16	12	13	15	22	23	18	19	20	21
3	0	1	4	5	2	8	11	6	10	9	7	14	17	12	16	15	13	19	20	21	22	23	18
4	3	0	5	2	1	9	10	7	11	8	6	15	16	13	17	14	12	20	21	22	23	18	19
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	7	11	8	9	10	0	1	3	4	5	2	18	19	23	22	21	20	12	13	17	16	15	14
7	11	10	6	8	9	1	0	4	3	2	5	19	18	22	23	20	21	14	12	13	17	16	15
8	6	7	9	10	11	3	2	0	5	4	1	23	20	18	21	22	19	13	17	16	15	14	12
9	8	6	10	11	7	4	5	1	2	3	0	22	21	19	20	23	18	17	16	15	14	12	13
10	9	8	11	7	6	5	4	2	1	0	3	21	22	20	19	18	23	16	15	14	12	13	17
11	10	9	7	6	8	2	3	5	0	1	4	20	23	21	18	19	22	15	14	12	13	17	16
12	13	17	14	15	16	18	19	23	22	21	20	0	1	3	4	5	2	6	7	11	10	9	8
13	17	16	12	14	15	19	18	22	23	20	21	1	0	4	3	2	5	8	6	7	11	10	9
14	12	13	15	16	17	23	20	18	21	22	19	3	2	0	5	4	1	7	11	10	9	8	6
15	14	12	16	17	13	22	21	19	20	23	18	4	5	1	2	3	0	11	10	9	8	6	7
16	15	14	17	13	12	21	22	20	19	18	23	5	4	2	1	0	3	10	9	8	6	7	11
17	16	15	13	12	14	20	23	21	18	19	22	2	3	5	0	1	4	9	8	6	7	11	10
18	19	20	23	22	21	12	13	14	15	16	17	6	7	8	9	10	11	0	1	2	5	4	3
19	20	21	18	23	22	13	12	15	14	17	16	7	6	9	8	11	10	3	0	1	2	5	4
20	21	22	19	18	23	17	14	16	12	13	15	11	8	10	6	7	9	4	3	0	1	2	5
21	22	23	20	19	18	16	15	17	13	12	14	10	9	11	7	6	8	5	4	3	0	1	2
22	23	18	21	20	19	15	16	13	17	14	12	9	10	7	11	8	6	2	5	4	3	0	1
23	18	19	22	21	20	14	17	12	16	15	13	8	11	6	10	9	7	1	2	5	4	3	0

Centre: 0

Centrum: 0 5 6 12

Nucleus: 0 21

Left Nucleus: 0 5 6 10 12 16 18 21

Middle Nucleus: 0 2 4 19 21 23

Right Nucleus: 0 2 4 19 21 23

1 Element of order 1: 0

15 Elements of order 2: 5 6 7 8 10 12 13 14 16 18 19 20 21 22 23

2 Elements of order 3: 2 4

6 Elements of order 6: 1 3 9 11 15 17

Commutator Subloop: 0 2 4

Associator Subloop: 0 2 4

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 2:

7 Conjugacy Classes of size 3:

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

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

A_l Property: FAILS. The left inner mapping L_1,1 = (6,9,11)(7,10,8)(12,15,17)(13,16,14) is not an automorphism. L_1,1(1*6) neq L_1,1(1)*L_1,1(6)

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

Right (Left, Full) Mult Group Orders: 48 (648, 3888)

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