Group 27.26.3.0 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	5	3	7	8	6	10	12	16	9	14	15	13	17	11	19	20	18	26	21	24	25	23	22
2	0	1	5	3	4	8	6	7	12	9	17	10	15	13	14	11	16	20	18	19	22	26	25	23	24	21
3	4	5	6	7	8	0	1	2	14	15	10	13	16	17	11	12	9	21	26	22	23	25	18	19	20	24
4	5	3	7	8	6	1	2	0	15	13	12	14	17	11	16	9	10	26	22	21	24	23	19	20	18	25
5	3	4	8	6	7	2	0	1	13	14	9	15	11	16	17	10	12	22	21	26	25	24	20	18	19	23
6	7	8	0	1	2	3	4	5	17	11	15	16	12	9	10	13	14	23	24	25	18	20	21	26	22	19
7	8	6	1	2	0	4	5	3	11	16	13	17	9	10	12	14	15	24	25	23	19	18	26	22	21	20
8	6	7	2	0	1	5	3	4	16	17	14	11	10	12	9	15	13	25	23	24	20	19	22	21	26	18
9	11	13	14	10	16	17	15	12	18	24	26	22	25	21	19	20	23	0	7	5	3	8	6	4	2	1
10	16	14	15	12	17	11	13	9	19	25	22	21	23	26	20	18	24	1	8	3	4	6	7	5	0	2
11	13	9	10	16	14	15	12	17	24	22	20	18	21	19	25	23	26	7	5	0	1	3	4	2	6	8
12	17	15	13	9	11	16	14	10	20	23	21	26	24	22	18	19	25	2	6	4	5	7	8	3	1	0
13	9	11	16	14	10	12	17	15	22	18	23	24	19	25	21	26	20	5	0	7	8	1	2	6	4	3
14	10	16	17	15	12	9	11	13	21	19	24	25	20	23	26	22	18	3	1	8	6	2	0	7	5	4
15	12	17	11	13	9	10	16	14	26	20	25	23	18	24	22	21	19	4	2	6	7	0	1	8	3	5
16	14	10	12	17	15	13	9	11	25	21	18	19	26	20	23	24	22	8	3	1	2	4	5	0	7	6
17	15	12	9	11	13	14	10	16	23	26	19	20	22	18	24	25	21	6	4	2	0	5	3	1	8	7
18	26	25	21	24	20	23	19	22	0	4	1	8	2	3	7	5	6	9	15	16	14	12	17	10	13	11
19	22	23	26	25	18	24	20	21	1	5	2	6	0	4	8	3	7	10	13	17	15	9	11	12	14	16
20	21	24	22	23	19	25	18	26	2	3	0	7	1	5	6	4	8	12	14	11	13	10	16	9	15	17
21	24	20	23	19	22	18	26	25	3	7	4	2	5	6	1	8	0	14	11	12	17	13	9	15	16	10
22	23	19	25	18	26	20	21	24	5	6	3	1	4	8	0	7	2	13	17	10	16	15	12	14	11	9
23	19	22	18	26	25	21	24	20	6	1	7	5	8	0	4	2	3	17	10	13	9	16	14	11	12	15
24	20	21	19	22	23	26	25	18	7	2	8	3	6	1	5	0	4	11	12	14	10	17	15	16	9	13
25	18	26	20	21	24	22	23	19	8	0	6	4	7	2	3	1	5	16	9	15	12	11	13	17	10	14
26	25	18	24	20	21	19	22	23	4	8	5	0	3	7	2	6	1	15	16	9	11	14	10	13	17	12

Centre: 0 3 6

Centrum: 0 3 6

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

26 Elements of order 3: 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

Commutator Subloop: 0 3 6

Associator Subloop: 0

3 Conjugacy Classes of size 1:

0
3
6

8 Conjugacy Classes of size 3:

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

Automorphic Inverse Property: FAILS. (1^-1)(10^-1) neq (1*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