Right Bol Loop 27.2.3.0 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	15	12	16	13	17	14	19	26	25	20	23	24	22	21	18
2	0	1	5	3	4	8	6	7	11	9	10	13	15	17	12	14	16	26	18	21	25	24	22	23	20	19
3	4	5	6	7	8	1	2	0	12	15	13	14	17	10	16	11	9	25	21	22	24	18	19	26	23	20
4	5	3	7	8	6	2	0	1	15	13	12	16	14	11	17	9	10	21	20	23	22	19	26	18	24	25
5	3	4	8	6	7	0	1	2	13	12	15	17	16	9	14	10	11	20	25	24	23	26	18	19	22	21
6	7	8	1	2	0	4	5	3	14	16	17	10	9	15	11	13	12	23	24	18	26	25	21	20	19	22
7	8	6	2	0	1	5	3	4	16	17	14	11	10	13	9	12	15	24	22	19	18	21	20	25	26	23
8	6	7	0	1	2	3	4	5	17	14	16	9	11	12	10	15	13	22	23	26	19	20	25	21	18	24
9	10	11	12	15	13	14	16	17	18	19	26	21	25	22	20	23	24	1	2	5	4	7	8	6	3	0
10	11	9	15	13	12	16	17	14	19	26	18	20	21	23	25	24	22	2	0	3	5	8	6	7	4	1
11	9	10	13	12	15	17	14	16	26	18	19	25	20	24	21	22	23	0	1	4	3	6	7	8	5	2
12	15	13	14	16	17	10	11	9	25	21	20	24	23	18	22	19	26	4	5	8	7	2	0	1	6	3
13	12	15	17	14	16	9	10	11	20	25	21	23	22	26	24	18	19	3	4	7	6	1	2	0	8	5
14	16	17	10	11	9	15	13	12	23	24	22	26	19	25	18	21	20	7	8	0	2	5	3	4	1	6
15	13	12	16	17	14	11	9	10	21	20	25	22	24	19	23	26	18	5	3	6	8	0	1	2	7	4
16	17	14	11	9	10	13	12	15	24	22	23	18	26	21	19	20	25	8	6	1	0	3	4	5	2	7
17	14	16	9	10	11	12	15	13	22	23	24	19	18	20	26	25	21	6	7	2	1	4	5	3	0	8
18	19	26	20	25	21	24	22	23	1	2	0	5	4	6	3	7	8	10	11	12	13	14	16	17	15	9
19	26	18	25	21	20	22	23	24	2	0	1	3	5	7	4	8	6	11	9	15	12	16	17	14	13	10
20	25	21	24	22	23	19	26	18	3	4	5	7	6	0	8	1	2	12	15	17	16	9	10	11	14	13
21	20	25	23	24	22	18	19	26	5	3	4	6	8	2	7	0	1	13	12	16	14	11	9	10	17	15
22	23	24	26	18	19	21	20	25	6	7	8	2	1	3	0	4	5	14	16	9	11	12	15	13	10	17
23	24	22	18	19	26	20	25	21	7	8	6	0	2	4	1	5	3	16	17	10	9	15	13	12	11	14
24	22	23	19	26	18	25	21	20	8	6	7	1	0	5	2	3	4	17	14	11	10	13	12	15	9	16
25	21	20	22	23	24	26	18	19	4	5	3	8	7	1	6	2	0	15	13	14	17	10	11	9	16	12
26	18	19	21	20	25	23	24	22	0	1	2	4	3	8	5	6	7	9	10	13	15	17	14	16	12	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 15
14 16 17
18 19 26
20 21 25
22 23 24

Automorphic Inverse Property: FAILS. (3^-1)(10^-1) neq (3*10)^-1

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