Group 28.1.2.0 of order 28

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	27
1	26	16	24	19	20	23	15	27	0	25	18	21	17	22	10	8	3	6	14	12	5	4	11	13	7	9	2
2	15	26	16	24	19	20	23	0	25	18	21	22	27	17	9	13	4	7	12	11	6	5	10	14	1	8	3
3	23	15	26	16	24	19	20	25	18	21	22	17	0	27	8	14	5	1	11	10	7	6	9	12	2	13	4
4	20	23	15	26	16	24	19	18	21	22	17	27	25	0	13	12	6	2	10	9	1	7	8	11	3	14	5
5	19	20	23	15	26	16	24	21	22	17	27	0	18	25	14	11	7	3	9	8	2	1	13	10	4	12	6
6	24	19	20	23	15	26	16	22	17	27	0	25	21	18	12	10	1	4	8	13	3	2	14	9	5	11	7
7	16	24	19	20	23	15	26	17	27	0	25	18	22	21	11	9	2	5	13	14	4	3	12	8	6	10	1
8	25	0	27	17	22	21	18	26	15	23	20	19	16	24	1	3	14	10	5	6	11	12	7	4	9	2	13
9	0	27	17	22	21	18	25	16	26	15	23	20	24	19	7	2	13	11	4	5	12	14	6	3	10	1	8
10	27	17	22	21	18	25	0	24	16	26	15	23	19	20	6	1	8	12	3	4	14	13	5	2	11	7	9
11	17	22	21	18	25	0	27	19	24	16	26	15	20	23	5	7	9	14	2	3	13	8	4	1	12	6	10
12	22	21	18	25	0	27	17	20	19	24	16	26	23	15	4	6	10	13	1	2	8	9	3	7	14	5	11
13	18	25	0	27	17	22	21	15	23	20	19	24	26	16	2	4	12	9	6	7	10	11	1	5	8	3	14
14	21	18	25	0	27	17	22	23	20	19	24	16	15	26	3	5	11	8	7	1	9	10	2	6	13	4	12
15	8	13	14	12	11	10	9	3	2	1	7	6	4	5	18	0	16	20	17	22	19	24	21	27	23	25	26
16	10	9	8	13	14	12	11	1	7	6	5	4	2	3	0	17	19	15	21	18	23	20	25	22	26	27	24
17	6	7	1	2	3	4	5	10	11	12	14	13	9	8	16	19	21	0	23	15	25	18	26	20	27	24	22
18	3	4	5	6	7	1	2	14	13	8	9	10	12	11	20	15	0	22	16	24	17	27	19	26	21	23	25
19	12	11	10	9	8	13	14	6	5	4	3	2	7	1	17	21	23	16	25	0	26	15	27	18	24	22	20
20	14	12	11	10	9	8	13	5	4	3	2	1	6	7	22	18	15	24	0	27	16	26	17	25	19	21	23
21	4	5	6	7	1	2	3	12	14	13	8	9	11	10	19	23	25	17	26	16	27	0	24	15	22	20	18
22	5	6	7	1	2	3	4	11	12	14	13	8	10	9	24	20	18	27	15	26	0	25	16	23	17	19	21
23	13	14	12	11	10	9	8	4	3	2	1	7	5	6	21	25	26	19	27	17	24	16	22	0	20	18	15
24	11	10	9	8	13	14	12	7	6	5	4	3	1	2	27	22	20	26	18	25	15	23	0	21	16	17	19
25	2	3	4	5	6	7	1	13	8	9	10	11	14	12	23	26	27	21	24	19	22	17	20	16	18	15	0
26	9	8	13	14	12	11	10	2	1	7	6	5	3	4	25	27	24	23	22	21	20	19	18	17	15	0	16
27	7	1	2	3	4	5	6	9	10	11	12	14	8	13	26	24	22	25	20	23	18	21	15	19	0	16	17

Centre: 0 26

Centrum: 0 26

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 27

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 27

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 27

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 27

1 Element of order 1: 0

1 Element of order 2: 26

14 Elements of order 4: 1 2 3 4 5 6 7 8 9 10 11 12 13 14

6 Elements of order 7: 17 18 21 22 25 27

6 Elements of order 14: 15 16 19 20 23 24

Commutator Subloop: 0 17 18 21 22 25 27

Associator Subloop: 0

2 Conjugacy Classes of size 1:

0
26

6 Conjugacy Classes of size 2:

15 16
17 18
19 20
21 22
23 24
25 27

2 Conjugacy Classes of size 7:

1 2 3 4 5 6 7
8 9 10 11 12 13 14

Automorphic Inverse Property: FAILS. (1^-1)(3^-1) neq (1*3)^-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: 28 (28, 392)

/ revised November, 2001