Right Bol Loop 24.17.1.0 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	16	17	14	15	23	13	20	22	0	19	21	18	6	8	7	5	2	12	4	11	3	10	9
2	17	16	15	14	18	0	22	20	13	21	19	23	9	7	8	12	1	5	3	10	4	11	6
3	19	21	0	13	20	15	23	18	14	16	17	22	8	6	9	10	4	11	2	12	1	5	7
4	21	19	13	0	22	14	18	23	15	17	16	20	7	9	6	11	3	10	1	5	2	12	8
5	23	18	20	22	0	17	19	21	16	14	15	13	12	11	10	9	6	2	8	4	7	3	1
6	13	0	21	19	17	23	15	14	18	22	20	16	1	3	4	2	5	9	10	7	11	8	12
7	14	15	16	17	19	22	0	13	20	23	18	21	4	2	1	3	11	8	12	6	5	9	10
8	15	14	17	16	21	20	13	0	22	18	23	19	3	1	2	4	10	7	5	9	12	6	11
9	0	13	19	21	16	18	14	15	23	20	22	17	2	4	3	1	12	6	11	8	10	7	5
10	20	22	23	18	14	21	16	17	19	0	13	15	11	12	5	7	8	4	6	2	9	1	3
11	22	20	18	23	15	19	17	16	21	13	0	14	10	5	12	8	7	3	9	1	6	2	4
12	18	23	22	20	13	16	21	19	17	15	14	0	5	10	11	6	9	1	7	3	8	4	2
13	2	1	4	3	12	9	8	7	6	11	10	5	0	15	14	17	16	23	21	22	19	20	18
14	3	4	1	2	10	8	9	6	7	5	12	11	15	0	13	19	21	22	16	23	17	18	20
15	4	3	2	1	11	7	6	9	8	12	5	10	14	13	0	21	19	20	17	18	16	23	22
16	5	12	7	8	9	2	10	11	1	3	4	6	18	20	22	23	13	17	14	19	15	21	0
17	12	5	8	7	6	1	11	10	2	4	3	9	23	22	20	18	0	16	15	21	14	19	13
18	6	9	11	10	2	5	4	3	12	8	7	1	16	21	19	13	23	0	22	15	20	14	17
19	10	11	9	6	7	4	5	12	3	1	2	8	22	23	18	20	15	21	0	16	13	17	14
20	7	8	5	12	3	11	1	2	10	9	6	4	21	16	17	14	22	15	23	0	18	13	19
21	11	10	6	9	8	3	12	5	4	2	1	7	20	18	23	22	14	19	13	17	0	16	15
22	8	7	12	5	4	10	2	1	11	6	9	3	19	17	16	15	20	14	18	13	23	0	21
23	9	6	10	11	1	12	3	4	5	7	8	2	17	19	21	0	18	13	20	14	22	15	16

Centre: 0

Centrum: 0

Nucleus: 0

Left Nucleus: 0 13 14 15

Middle Nucleus: 0 16 23

Right Nucleus: 0 16 23

1 Element of order 1: 0

17 Elements of order 2: 3 4 5 7 8 10 11 12 13 14 15 17 18 19 20 21 22

2 Elements of order 3: 16 23

4 Elements of order 6: 1 2 6 9

Commutator Subloop: 0 13 16 17 18 23

Associator Subloop: 0 13 16 17 18 23

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 2:

16 23

1 Conjugacy Class of size 3:

13 17 18

3 Conjugacy Classes of size 6:

1 2 5 6 9 12
3 4 7 8 10 11
14 15 19 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 = (2,6,12)(3,4)(7,8)(10,11)(13,17,18)(14,15)(19,21)(20,22) 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: 96 (69984, 279936)

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

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

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