Right Bol Loop 27.20.3.0 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	7	12	23	3	9	15	14	13	25	17	16	8	10	11	6	24	19	22	26	18	20	5	21
2	0	1	6	23	3	5	18	10	14	17	9	4	15	11	16	13	8	25	20	24	26	21	12	19	7	22
3	5	7	8	17	9	10	11	0	1	19	2	15	24	26	22	21	20	16	6	4	18	12	13	23	14	25
4	6	23	9	15	10	8	14	1	22	26	24	13	20	21	0	19	2	11	25	12	7	3	17	18	16	5
5	7	3	16	10	11	14	13	21	19	24	0	8	1	20	26	2	22	15	23	6	12	25	9	4	17	18
6	23	4	10	13	8	9	16	2	24	1	21	17	19	22	20	0	26	14	18	25	3	5	15	12	11	7
7	3	5	11	8	14	16	17	22	0	21	20	9	2	19	1	26	24	13	4	23	25	18	10	6	15	12
8	16	10	0	1	21	22	19	3	18	12	6	2	23	25	7	4	5	20	15	9	17	11	24	13	26	14
9	15	13	1	19	2	24	0	4	12	23	3	26	18	5	25	6	7	22	14	11	10	8	20	17	21	16
10	8	16	2	26	24	1	21	6	23	18	4	20	12	7	5	3	25	0	9	13	14	17	19	15	22	11
11	14	17	22	24	0	21	20	7	3	4	5	1	6	12	18	25	23	26	16	8	13	9	2	10	19	15
12	25	18	15	14	13	17	9	19	26	20	1	16	22	2	21	24	0	8	5	3	23	4	11	7	10	6
13	9	15	24	20	1	2	22	23	5	7	12	19	25	3	6	18	4	21	11	17	16	10	26	14	0	8
14	17	11	26	21	20	19	2	25	4	6	7	22	3	23	12	5	18	1	10	16	9	15	0	8	24	13
15	13	9	19	0	26	20	1	12	25	5	18	21	7	6	4	23	3	24	17	14	8	16	22	11	2	10
16	10	8	21	2	22	0	26	5	6	3	25	24	4	18	23	7	12	19	13	15	11	14	1	9	20	17
17	11	14	20	22	19	26	24	18	7	25	23	0	5	4	3	12	6	2	8	10	15	13	21	16	1	9
18	12	25	17	11	15	13	8	20	2	0	26	14	21	1	24	22	19	10	3	7	6	23	16	5	9	4
19	24	20	12	25	23	4	5	15	8	16	17	18	11	10	9	14	13	3	21	26	0	1	7	22	6	2
20	19	24	18	6	7	25	23	17	11	8	14	3	16	9	13	15	10	12	26	22	2	0	5	21	4	1
21	22	26	5	12	6	3	25	16	10	13	8	23	9	17	14	11	15	7	0	2	19	24	4	1	18	20
22	26	21	7	3	25	18	4	11	13	9	16	5	10	15	17	8	14	23	1	0	24	20	6	2	12	19
23	4	6	13	16	17	15	10	24	20	22	19	11	26	0	2	1	21	9	12	18	5	7	14	25	8	3
24	20	19	23	18	4	12	6	13	17	15	10	7	14	8	11	9	16	5	22	21	1	2	25	26	3	0
25	18	12	14	9	16	11	15	26	21	2	22	10	0	24	19	20	1	17	7	5	4	6	8	3	13	23
26	21	22	25	5	18	7	12	14	16	11	15	6	8	13	10	17	9	4	2	1	20	19	3	0	23	24

Centre: 0 24 26

Centrum: 0 24 26

Nucleus: 0 24 26

Left Nucleus: 0 6 7 9 12 16 17 24 26

Middle Nucleus: 0 24 26

Right Nucleus: 0 24 26

1 Element of order 1: 0

20 Elements of order 3: 1 2 3 4 5 8 10 11 13 14 15 18 19 20 21 22 23 24 25 26

6 Elements of order 9: 6 7 9 12 16 17

Commutator Subloop: 0 24 26

Associator Subloop: 0 24 26

3 Conjugacy Classes of size 1:

0
24
26

8 Conjugacy Classes of size 3:

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

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