Right Bol Loop 27.8.3.0 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	11	6	15	18	17	16	8	3	14	7	19	5	20	10	13	12	9	22	26	24	25	23	21
2	0	1	6	15	19	12	17	16	18	9	5	3	8	4	14	13	20	10	11	7	26	21	25	23	24	22
3	5	6	7	8	18	9	22	1	21	0	13	20	2	17	16	25	24	26	10	23	14	15	4	11	19	12
4	11	19	18	9	17	10	26	24	25	1	16	13	22	7	20	23	0	2	8	21	3	5	14	15	12	6
5	6	3	20	17	13	7	23	2	0	26	10	9	25	16	8	1	22	21	18	24	15	12	11	19	4	14
6	3	5	17	10	7	8	21	22	1	2	20	16	23	18	13	24	26	25	9	0	12	14	19	4	11	15
7	20	13	22	26	23	2	15	12	6	3	24	1	11	21	25	19	14	4	0	5	9	16	18	17	10	8
8	9	16	1	21	24	22	4	14	19	12	0	2	15	25	26	5	3	11	23	6	10	18	13	7	20	17
9	16	8	2	25	0	1	6	15	12	11	23	22	5	26	21	14	4	19	24	3	18	17	7	20	13	10
10	18	17	0	1	26	24	3	5	11	19	21	23	14	2	22	15	6	12	25	4	13	7	8	9	16	20
11	19	4	9	16	10	20	2	0	23	24	18	7	26	8	17	21	1	22	13	25	5	6	15	12	14	3
12	14	15	8	13	9	16	1	21	22	23	7	17	0	10	18	26	25	24	20	2	19	4	6	3	5	11
13	7	20	24	22	25	23	11	3	5	14	26	0	4	1	2	6	12	15	21	19	8	9	10	18	17	16
14	15	12	13	7	16	18	24	25	26	21	8	10	1	20	9	2	23	0	17	22	4	11	3	5	6	19
15	12	14	16	18	20	17	25	26	24	22	9	8	21	13	10	0	2	23	7	1	11	19	5	6	3	4
16	8	9	25	23	1	21	19	4	14	15	2	26	6	24	0	3	11	5	22	12	17	10	20	13	7	18
17	10	18	21	0	22	26	14	19	4	6	1	25	12	23	24	11	5	3	2	15	20	13	16	8	9	7
18	17	10	26	24	2	25	5	11	3	4	22	21	19	0	23	12	15	6	1	14	7	20	9	16	8	13
19	4	11	10	20	8	13	0	23	2	25	17	18	24	9	7	22	21	1	16	26	6	3	12	14	15	5
20	13	7	23	2	21	0	12	6	15	5	25	24	3	22	1	4	19	14	26	11	16	8	17	10	18	9
21	22	26	14	19	3	4	13	10	20	17	12	15	18	5	11	9	8	7	6	16	23	24	0	1	2	25
22	26	21	15	5	12	14	16	18	17	7	6	4	9	11	19	10	13	20	3	8	24	25	1	2	0	23
23	24	25	12	14	11	3	8	9	7	20	19	6	10	15	4	18	16	17	5	13	0	1	21	22	26	2
24	25	23	11	3	15	5	9	7	8	13	4	19	20	12	6	17	18	16	14	10	1	2	22	26	21	0
25	23	24	19	12	4	11	10	20	13	16	14	5	17	6	3	7	9	8	15	18	2	0	26	21	22	1
26	21	22	5	6	14	19	20	13	10	18	15	11	16	3	12	8	7	9	4	17	25	23	2	0	1	24

Centre: 0 22 25

Centrum: 0 22 25

Nucleus: 0 22 25

Left Nucleus: 0 4 5 9 12 13 17 22 25

Middle Nucleus: 0 22 25

Right Nucleus: 0 22 25

1 Element of order 1: 0

8 Elements of order 3: 1 2 21 22 23 24 25 26

18 Elements of order 9: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Commutator Subloop: 0 22 25

Associator Subloop: 0 22 25

3 Conjugacy Classes of size 1:

0
22
25

8 Conjugacy Classes of size 3:

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

Automorphic Inverse Property: FAILS. (1^-1)(4^-1) neq (1*4)^-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