Right Bol Loop 24.9.4.0 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	18	13	15	19	17	23	20	21	14	22	16	0	2	6	3	4	5	9	12	7	8	10	11
2	22	0	16	20	14	21	19	23	17	18	15	13	6	5	1	3	4	10	7	9	12	11	8
3	20	14	0	21	16	22	18	19	13	23	17	15	1	2	4	5	6	7	8	12	11	9	10
4	19	17	13	23	15	18	22	20	0	21	14	16	3	1	5	6	2	12	11	8	10	7	9
5	21	16	14	22	0	20	23	18	15	19	13	17	4	3	6	2	1	8	10	11	9	12	7
6	23	15	17	18	13	19	21	22	16	20	0	14	5	4	2	1	3	11	9	10	7	8	12
7	13	18	19	15	23	17	0	16	22	14	21	20	9	10	12	8	11	2	3	1	4	6	5
8	15	23	18	17	19	13	14	0	20	16	22	21	12	7	11	10	9	3	5	4	6	1	2
9	14	20	21	0	22	16	15	17	23	13	19	18	10	11	7	12	8	6	1	2	3	5	4
10	17	19	23	13	18	15	16	14	21	0	20	22	11	8	9	7	12	5	2	6	1	4	3
11	16	21	22	14	20	0	17	13	19	15	18	23	8	12	10	9	7	4	6	5	2	3	1
12	0	22	20	16	21	14	13	15	18	17	23	19	7	9	8	11	10	1	4	3	5	2	6
13	2	1	4	3	6	5	12	11	10	9	8	7	14	17	0	15	16	22	20	18	19	23	21
14	6	3	5	1	2	4	8	10	11	7	12	9	17	16	13	0	15	23	18	22	20	21	19
15	3	6	1	5	4	2	9	12	7	11	10	8	0	13	16	17	14	20	21	19	23	18	22
16	4	5	2	6	3	1	10	7	12	8	9	11	15	0	17	14	13	19	23	21	22	20	18
17	5	4	6	2	1	3	11	9	8	12	7	10	16	15	14	13	0	21	22	23	18	19	20
18	9	7	8	12	10	11	3	5	6	2	4	1	22	23	20	19	21	14	0	13	15	17	16
19	12	10	7	11	8	9	2	3	1	5	6	4	20	18	21	23	22	0	16	15	17	13	14
20	7	9	12	8	11	10	1	4	2	6	5	3	18	22	19	21	23	13	15	0	16	14	17
21	8	11	9	10	12	7	6	1	3	4	2	5	19	20	23	22	18	15	17	16	14	0	13
22	10	12	11	7	9	8	4	6	5	1	3	2	23	21	18	20	19	17	13	14	0	16	15
23	11	8	10	9	7	12	5	2	4	3	1	6	21	19	22	18	20	16	14	17	13	15	0

Centre: 0 23

Centrum: 0 17 20 23

Nucleus: 0 23

Left Nucleus: 0 17 20 23

Middle Nucleus: 0 14 16 18 19 23

Right Nucleus: 0 14 16 18 19 23

1 Element of order 1: 0

9 Elements of order 2: 2 3 5 7 8 10 17 20 23

2 Elements of order 3: 14 16

2 Elements of order 4: 4 9

6 Elements of order 6: 13 15 18 19 21 22

4 Elements of order 12: 1 6 11 12

Commutator Subloop: 0 14 16 18 19 23

Associator Subloop: 0 14 16 18 19 23

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

14 16
18 19

3 Conjugacy Classes of size 6:

1 4 6 9 11 12
2 3 5 7 8 10
13 15 17 20 21 22

Automorphic Inverse Property: FAILS. (1^-1)(3^-1) neq (1*3)^-1

A_l Property: FAILS. The left inner mapping L_1,1 = (2,10,5,8,3,7)(13,20,15,21,17,22) is not an automorphism. L_1,1(1*2) neq L_1,1(1)*L_1,1(2)

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