Right Bol Loop 27.2.3.1 of order 27

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
1	2	0	4	5	3	7	8	6	10	11	9	13	14	12	16	17	15	19	26	25	20	23	24	22	21	18
2	0	1	5	3	4	8	6	7	11	9	10	14	12	13	17	15	16	26	18	21	25	24	22	23	20	19
3	4	5	6	7	8	1	2	0	12	13	14	15	16	17	10	11	9	25	21	22	24	18	19	26	23	20
4	5	3	7	8	6	2	0	1	13	14	12	16	17	15	11	9	10	21	20	23	22	19	26	18	24	25
5	3	4	8	6	7	0	1	2	14	12	13	17	15	16	9	10	11	20	25	24	23	26	18	19	22	21
6	7	8	1	2	0	4	5	3	15	16	17	10	11	9	13	14	12	23	24	18	26	25	21	20	19	22
7	8	6	2	0	1	5	3	4	16	17	15	11	9	10	14	12	13	24	22	19	18	21	20	25	26	23
8	6	7	0	1	2	3	4	5	17	15	16	9	10	11	12	13	14	22	23	26	19	20	25	21	18	24
9	10	11	13	14	12	17	15	16	18	19	26	20	25	21	24	22	23	1	2	3	5	6	7	8	4	0
10	11	9	14	12	13	15	16	17	19	26	18	25	21	20	22	23	24	2	0	4	3	7	8	6	5	1
11	9	10	12	13	14	16	17	15	26	18	19	21	20	25	23	24	22	0	1	5	4	8	6	7	3	2
12	13	14	16	17	15	9	10	11	25	21	20	22	23	24	26	18	19	4	5	6	8	1	2	0	7	3
13	14	12	17	15	16	10	11	9	21	20	25	23	24	22	18	19	26	5	3	7	6	2	0	1	8	4
14	12	13	15	16	17	11	9	10	20	25	21	24	22	23	19	26	18	3	4	8	7	0	1	2	6	5
15	16	17	11	9	10	12	13	14	23	24	22	18	19	26	20	25	21	7	8	1	0	4	5	3	2	6
16	17	15	9	10	11	13	14	12	24	22	23	19	26	18	25	21	20	8	6	2	1	5	3	4	0	7
17	15	16	10	11	9	14	12	13	22	23	24	26	18	19	21	20	25	6	7	0	2	3	4	5	1	8
18	19	26	21	20	25	22	23	24	1	2	0	4	5	3	7	8	6	10	11	14	13	16	17	15	12	9
19	26	18	20	25	21	23	24	22	2	0	1	5	3	4	8	6	7	11	9	12	14	17	15	16	13	10
20	25	21	23	24	22	26	18	19	3	4	5	6	7	8	1	2	0	12	13	16	15	10	11	9	17	14
21	20	25	22	23	24	19	26	18	5	3	4	8	6	7	0	1	2	14	12	15	17	9	10	11	16	13
22	23	24	19	26	18	20	25	21	6	7	8	1	2	0	4	5	3	15	16	11	10	13	14	12	9	17
23	24	22	26	18	19	25	21	20	7	8	6	2	0	1	5	3	4	16	17	9	11	14	12	13	10	15
24	22	23	18	19	26	21	20	25	8	6	7	0	1	2	3	4	5	17	15	10	9	12	13	14	11	16
25	21	20	24	22	23	18	19	26	4	5	3	7	8	6	2	0	1	13	14	17	16	11	9	10	15	12
26	18	19	25	21	20	24	22	23	0	1	2	3	4	5	6	7	8	9	10	13	12	15	16	17	14	11

Centre: 0 1 2

Centrum: 0 1 2

Nucleus: 0 1 2

Left Nucleus: 0 1 2 3 4 5 6 7 8

Middle Nucleus: 0 1 2

Right Nucleus: 0 1 2

1 Element of order 1: 0

2 Elements of order 3: 1 2

24 Elements of order 9: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Commutator Subloop: 0 1 2

Associator Subloop: 0 1 2

3 Conjugacy Classes of size 1:

0
1
2

8 Conjugacy Classes of size 3:

3 4 5
6 7 8
9 10 11
12 13 14
15 16 17
18 19 26
20 21 25
22 23 24

Automorphic Inverse Property: HOLDS

A_l Property: HOLDS (i.e. every left inner mapping L_a,b is an automorphism)

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

Right (Left, Full) Mult Group Orders: 81 (243, 2187)

/ revised October, 2001