Group 27.8.3.2 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	13	14	12	16	17	15	19	20	18	26	21	24	25	23	22
2	0	1	5	3	4	8	6	7	11	9	10	14	12	13	17	15	16	20	18	19	22	26	25	23	24	21
3	4	5	6	7	8	1	2	0	12	13	14	15	16	17	10	11	9	21	26	22	23	25	19	20	18	24
4	5	3	7	8	6	2	0	1	13	14	12	16	17	15	11	9	10	26	22	21	24	23	20	18	19	25
5	3	4	8	6	7	0	1	2	14	12	13	17	15	16	9	10	11	22	21	26	25	24	18	19	20	23
6	7	8	1	2	0	4	5	3	15	16	17	10	11	9	13	14	12	23	24	25	19	18	26	22	21	20
7	8	6	2	0	1	5	3	4	16	17	15	11	9	10	14	12	13	24	25	23	20	19	22	21	26	18
8	6	7	0	1	2	3	4	5	17	15	16	9	10	11	12	13	14	25	23	24	18	20	21	26	22	19
9	10	11	13	14	12	17	15	16	18	19	20	26	22	21	25	23	24	0	1	2	4	3	8	6	7	5
10	11	9	14	12	13	15	16	17	19	20	18	22	21	26	23	24	25	1	2	0	5	4	6	7	8	3
11	9	10	12	13	14	16	17	15	20	18	19	21	26	22	24	25	23	2	0	1	3	5	7	8	6	4
12	13	14	16	17	15	9	10	11	21	26	22	24	25	23	18	19	20	3	4	5	7	6	0	1	2	8
13	14	12	17	15	16	10	11	9	26	22	21	25	23	24	19	20	18	4	5	3	8	7	1	2	0	6
14	12	13	15	16	17	11	9	10	22	21	26	23	24	25	20	18	19	5	3	4	6	8	2	0	1	7
15	16	17	11	9	10	12	13	14	23	24	25	20	18	19	21	26	22	6	7	8	2	1	3	4	5	0
16	17	15	9	10	11	13	14	12	24	25	23	18	19	20	26	22	21	7	8	6	0	2	4	5	3	1
17	15	16	10	11	9	14	12	13	25	23	24	19	20	18	22	21	26	8	6	7	1	0	5	3	4	2
18	19	20	22	21	26	24	25	23	0	1	2	5	3	4	7	8	6	9	10	11	14	13	16	17	15	12
19	20	18	21	26	22	25	23	24	1	2	0	3	4	5	8	6	7	10	11	9	12	14	17	15	16	13
20	18	19	26	22	21	23	24	25	2	0	1	4	5	3	6	7	8	11	9	10	13	12	15	16	17	14
21	26	22	25	23	24	20	18	19	3	4	5	8	6	7	2	0	1	12	13	14	17	16	11	9	10	15
22	21	26	24	25	23	19	20	18	5	3	4	7	8	6	1	2	0	14	12	13	16	15	10	11	9	17
23	24	25	18	19	20	22	21	26	6	7	8	0	1	2	5	3	4	15	16	17	9	11	14	12	13	10
24	25	23	19	20	18	21	26	22	7	8	6	1	2	0	3	4	5	16	17	15	10	9	12	13	14	11
25	23	24	20	18	19	26	22	21	8	6	7	2	0	1	4	5	3	17	15	16	11	10	13	14	12	9
26	22	21	23	24	25	18	19	20	4	5	3	6	7	8	0	1	2	13	14	12	15	17	9	10	11	16

Centre: 0 1 2

Centrum: 0 1 2

Nucleus: 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

Left Nucleus: 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

Middle Nucleus: 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

Right Nucleus: 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 Element of order 1: 0

8 Elements of order 3: 1 2 9 10 11 18 19 20

18 Elements of order 9: 3 4 5 6 7 8 12 13 14 15 16 17 21 22 23 24 25 26

Commutator Subloop: 0 1 2

Associator Subloop: 0

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 14
15 16 17
18 19 20
21 22 26
23 24 25

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: 27 (27, 243)

/ revised October, 2001