Right Bol Loop 24.19.2.0 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	21	23	22	20	18
2	5	4	1	0	3	11	10	7	6	8	9	17	16	13	12	14	15	21	22	18	20	23	19
3	0	1	4	5	2	8	6	9	10	11	7	14	12	15	16	17	13	23	18	22	19	21	20
4	3	0	5	2	1	9	8	10	11	7	6	15	14	16	17	13	12	20	23	21	18	19	22
5	4	3	2	1	0	10	9	11	7	6	8	16	15	17	13	12	14	22	20	19	23	18	21
6	8	9	7	11	10	0	3	1	2	5	4	18	19	23	20	22	21	12	13	15	17	16	14
7	6	8	11	10	9	1	0	2	5	4	3	23	18	20	22	21	19	14	12	16	13	17	15
8	9	10	6	7	11	3	4	0	1	2	5	19	21	18	23	20	22	13	17	14	16	15	12
9	10	11	8	6	7	4	5	3	0	1	2	21	22	19	18	23	20	17	16	12	15	14	13
10	11	7	9	8	6	5	2	4	3	0	1	22	20	21	19	18	23	16	15	13	14	12	17
11	7	6	10	9	8	2	1	5	4	3	0	20	23	22	21	19	18	15	14	17	12	13	16
12	14	15	13	17	16	18	19	23	20	22	21	0	3	1	2	5	4	6	7	9	11	10	8
13	12	14	17	16	15	23	18	20	22	21	19	1	0	2	5	4	3	8	6	10	7	11	9
14	15	16	12	13	17	19	21	18	23	20	22	3	4	0	1	2	5	7	11	8	10	9	6
15	16	17	14	12	13	21	22	19	18	23	20	4	5	3	0	1	2	11	10	6	9	8	7
16	17	13	15	14	12	22	20	21	19	18	23	5	2	4	3	0	1	10	9	7	8	6	11
17	13	12	16	15	14	20	23	22	21	19	18	2	1	5	4	3	0	9	8	11	6	7	10
18	23	20	19	21	22	12	13	14	15	16	17	6	7	8	9	10	11	0	3	2	4	5	1
19	18	23	21	22	20	14	12	15	16	17	13	8	6	9	10	11	7	1	0	5	3	4	2
20	22	21	23	18	19	17	16	13	12	14	15	11	10	7	6	8	9	4	5	0	2	1	3
21	19	18	22	20	23	15	14	16	17	13	12	9	8	10	11	7	6	2	1	4	0	3	5
22	21	19	20	23	18	16	15	17	13	12	14	10	9	11	7	6	8	5	2	3	1	0	4
23	20	22	18	19	21	13	17	12	14	15	16	7	11	6	8	9	10	3	4	1	5	2	0

Centre: 0 5

Centrum: 0 5

Nucleus: 0 5

Left Nucleus: 0 5 6 10 12 16 18 22

Middle Nucleus: 0 1 2 3 4 5

Right Nucleus: 0 1 2 3 4 5

1 Element of order 1: 0

19 Elements of order 2: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

2 Elements of order 3: 2 4

2 Elements of order 6: 1 3

Commutator Subloop: 0 2 4

Associator Subloop: 0 2 4

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

6 Conjugacy Classes of size 3:

6 9 11
7 8 10
12 15 17
13 14 16
18 20 21
19 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)(18,21,20)(19,22,23) 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 (648, 1296)

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