Right Bol Loop 27.8.3.1 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	11	19	15	12	14	16	8	3	17	6	10	13	18	7	9	20	5	22	23	21	26	24	25
2	0	1	5	19	13	4	14	16	12	9	20	10	3	18	11	17	8	7	6	15	23	21	22	25	26	24
3	4	6	7	18	14	17	24	21	22	0	9	1	12	2	10	23	25	26	16	8	13	5	15	19	11	20
4	6	3	12	17	7	16	26	25	0	1	10	22	14	24	8	21	23	2	18	9	5	15	13	20	19	11
5	15	13	14	16	12	18	25	0	26	2	8	24	7	21	9	22	1	23	17	10	19	20	11	6	4	3
6	3	4	17	10	18	8	22	24	21	25	12	23	16	1	14	2	26	0	9	7	15	13	5	11	20	19
7	8	14	24	21	22	2	19	4	11	3	25	20	26	5	0	15	6	13	23	1	18	9	10	16	17	12
8	14	7	1	22	0	24	4	11	19	13	23	5	25	15	21	20	3	6	26	2	9	10	18	12	16	17
9	10	18	2	0	21	1	5	15	20	11	26	3	23	13	22	6	4	19	25	24	16	12	17	14	8	7
10	18	9	0	26	25	22	3	13	6	15	2	4	1	11	23	19	5	20	24	21	12	17	16	7	14	8
11	19	20	9	7	8	12	2	23	1	22	18	0	10	26	17	25	21	24	14	16	3	4	6	5	13	15
12	17	16	26	2	24	23	20	5	15	4	0	6	22	3	1	13	19	11	21	25	14	7	8	18	10	9
13	5	15	8	14	10	7	1	2	23	21	16	25	9	0	18	26	24	22	12	17	11	19	20	4	3	6
14	7	8	25	24	1	26	6	3	13	5	21	19	0	4	2	11	20	15	22	23	10	18	9	17	12	16
15	13	5	10	12	9	14	0	26	25	23	17	21	8	22	16	24	2	1	7	18	20	11	19	3	6	4
16	12	17	23	1	2	25	15	20	5	19	22	13	21	6	24	3	11	4	0	26	8	14	7	10	9	18
17	16	12	22	23	26	21	11	19	4	6	1	15	24	20	25	5	13	3	2	0	7	8	14	9	18	10
18	9	10	21	25	23	0	13	6	3	20	24	11	2	19	26	4	15	5	1	22	17	16	12	8	7	14
19	20	11	16	8	17	9	23	1	2	24	14	26	18	25	7	0	22	21	10	12	4	6	3	15	5	13
20	11	19	18	9	16	10	21	22	24	26	7	2	17	23	12	1	0	25	8	14	6	3	4	13	15	5
21	22	23	13	6	3	19	8	9	7	18	15	14	5	16	20	12	10	17	4	11	25	24	26	1	0	2
22	23	21	11	3	20	13	9	7	8	17	4	16	15	12	6	14	18	10	5	19	24	26	25	2	1	0
23	21	22	15	13	11	5	10	18	17	16	6	8	20	9	19	7	14	12	3	4	26	25	24	0	2	1
24	26	25	19	20	6	11	16	12	14	7	5	18	4	17	3	10	9	8	15	13	1	2	0	23	22	21
25	24	26	6	15	4	20	17	10	18	14	13	7	19	8	5	9	12	16	11	3	0	1	2	22	21	23
26	25	24	20	5	15	3	18	17	10	12	19	9	11	7	4	8	16	14	13	6	2	0	1	21	23	22

Centre: 0 23 24

Centrum: 0 23 24

Nucleus: 0 23 24

Left Nucleus: 0 4 9 13 14 17 20 23 24

Middle Nucleus: 0 23 24

Right Nucleus: 0 23 24

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 23 24

Associator Subloop: 0 23 24

3 Conjugacy Classes of size 1:

0
23
24

8 Conjugacy Classes of size 3:

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

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