Right Bol Loop 27.14.3.0 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	6	15	3	14	9	10	8	16	13	18	19	20	17	11	12	7	5	25	24	21	26	23	22
2	0	1	6	3	20	4	19	10	8	9	17	18	12	7	5	11	16	13	14	15	23	26	25	22	21	24
3	5	7	8	9	11	10	12	0	21	22	1	2	23	13	16	25	24	26	18	17	4	6	14	20	15	19
4	15	14	9	10	16	8	13	1	25	24	2	0	21	18	17	23	26	22	12	11	6	3	19	5	20	7
5	7	3	11	16	12	17	8	26	2	23	22	24	1	9	13	0	21	25	10	18	15	20	4	19	14	6
6	20	19	10	8	17	9	18	2	23	26	0	1	25	12	11	21	22	24	13	16	3	4	7	15	5	14
7	3	5	12	13	8	18	11	25	24	1	23	21	22	16	9	26	2	0	17	10	14	19	15	6	4	20
8	9	10	0	26	21	25	22	3	19	15	4	6	14	23	2	7	20	5	1	24	18	16	13	17	12	11
9	10	8	1	22	25	23	24	4	7	20	6	3	19	21	0	14	5	15	2	26	12	17	18	11	13	16
10	8	9	2	24	23	21	26	6	14	5	3	4	7	25	1	19	15	20	0	22	13	11	12	16	18	17
11	16	17	26	25	2	0	23	5	6	14	15	20	4	1	24	3	19	7	22	21	10	13	9	18	8	12
12	13	18	25	0	24	26	1	7	20	4	14	19	15	22	21	5	6	3	23	2	17	9	16	10	11	8
13	18	12	23	1	26	22	2	14	5	6	19	7	20	24	25	15	3	4	21	0	11	10	17	8	16	9
14	4	15	13	18	9	12	16	23	26	2	21	25	24	17	10	22	0	1	11	8	19	7	20	3	6	5
15	14	4	16	17	13	11	9	22	0	21	24	26	2	10	18	1	25	23	8	12	20	5	6	7	19	3
16	17	11	22	23	0	1	21	15	3	19	20	5	6	2	26	4	7	14	24	25	8	18	10	12	9	13
17	11	16	24	21	1	2	25	20	4	7	5	15	3	0	22	6	14	19	26	23	9	12	8	13	10	18
18	12	13	21	2	22	24	0	19	15	3	7	14	5	26	23	20	4	6	25	1	16	8	11	9	17	10
19	6	20	18	12	10	13	17	21	22	0	25	23	26	11	8	24	1	2	16	9	7	14	5	4	3	15
20	19	6	17	11	18	16	10	24	1	25	26	22	0	8	12	2	23	21	9	13	5	15	3	14	7	4
21	25	23	19	7	6	14	20	18	12	13	10	17	11	5	3	8	9	16	15	4	22	0	26	1	24	2
22	24	26	15	20	14	5	4	16	17	11	13	9	10	6	19	18	12	8	3	7	0	21	2	25	1	23
23	21	25	14	19	4	7	15	13	18	12	9	16	17	20	6	10	8	11	5	3	26	2	24	0	22	1
24	26	22	20	5	19	15	6	17	11	16	18	10	8	3	7	12	13	9	4	14	1	25	0	23	2	21
25	23	21	7	14	3	19	5	12	13	18	8	11	16	15	4	9	10	17	20	6	24	1	22	2	26	0
26	22	24	5	15	7	20	3	11	16	17	12	8	9	4	14	13	18	10	6	19	2	23	1	21	0	25

Centre: 0 23 24

Centrum: 0 23 24

Nucleus: 0 23 24

Left Nucleus: 0 1 2 21 22 23 24 25 26

Middle Nucleus: 0 23 24

Right Nucleus: 0 23 24

1 Element of order 1: 0

14 Elements of order 3: 1 2 3 8 13 14 17 20 21 22 23 24 25 26

12 Elements of order 9: 4 5 6 7 9 10 11 12 15 16 18 19

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 14 20
4 5 19
6 7 15
8 13 17
9 11 18
10 12 16

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