Right Bol Loop 24.13.5.0 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	6	9	8	11	10	13	12	15	14	17	16	23	20	19	22	21	18
2	5	4	1	0	3	11	8	10	6	7	9	17	14	16	12	13	15	22	21	18	23	20	19
3	0	1	4	5	2	8	11	6	10	9	7	14	17	12	16	15	13	19	18	21	20	23	22
4	3	0	5	2	1	9	10	7	11	8	6	15	16	13	17	14	12	20	23	22	19	18	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	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	17	13	15	16	12
8	6	7	9	10	11	3	2	0	5	4	1	23	20	18	21	22	19	13	12	16	17	14	15
9	8	6	10	11	7	4	5	1	2	3	0	22	21	19	20	23	18	17	14	15	13	12	16
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	16	12	14	17	13
12	14	15	13	17	16	18	21	23	20	19	22	0	5	3	2	1	4	9	8	11	10	6	7
13	12	14	17	16	15	19	20	22	21	18	23	1	2	4	5	0	3	10	6	7	9	8	11
14	15	16	12	13	17	23	22	18	19	20	21	3	4	0	1	2	5	8	9	10	11	7	6
15	16	17	14	12	13	22	23	19	18	21	20	4	3	1	0	5	2	6	10	9	7	11	8
16	17	13	15	14	12	21	18	20	23	22	19	5	0	2	3	4	1	7	11	8	6	10	9
17	13	12	16	15	14	20	19	21	22	23	18	2	1	5	4	3	0	11	7	6	8	9	10
18	23	22	19	20	21	12	16	14	17	13	15	6	10	8	11	7	9	4	3	2	5	0	1
19	18	23	20	21	22	13	17	15	16	12	14	7	11	9	10	6	8	5	0	1	4	3	2
20	19	18	21	22	23	17	13	16	15	14	12	11	7	10	9	8	6	2	1	0	3	4	5
21	20	19	22	23	18	16	12	17	14	15	13	10	6	11	8	9	7	1	2	3	0	5	4
22	21	20	23	18	19	15	14	13	12	16	17	9	8	7	6	10	11	0	5	4	1	2	3
23	22	21	18	19	20	14	15	12	13	17	16	8	9	6	7	11	10	3	4	5	2	1	0

Centre: 0

Centrum: 0 5 6 14 20

Nucleus: 0

Left Nucleus: 0 5 6 10 14 17 20 23

Middle Nucleus: 0 2 4

Right Nucleus: 0 2 4

1 Element of order 1: 0

13 Elements of order 2: 5 6 7 8 10 12 14 15 17 19 20 21 23

2 Elements of order 3: 2 4

8 Elements of order 6: 1 3 9 11 13 16 18 22

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)(18,20,22)(19,23,21) 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 (17496, 34992)

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