Group 28.15.2.0 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	0	5	4	3	2	27	25	26	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	7	8	6
2	3	25	27	0	1	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	24	23	26
3	2	1	0	27	25	26	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	5	6	4
4	5	0	1	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	26	25	2	27	3
5	4	7	6	1	0	3	2	27	25	26	24	23	22	21	20	19	18	17	16	15	14	13	12	11	9	10	8
6	7	4	5	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	26	25	27	2	0	3	1
7	6	9	8	5	4	1	0	3	2	27	25	26	24	23	22	21	20	19	18	17	16	15	14	13	11	12	10
8	9	6	7	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	26	25	27	2	3	0	4	1	5
9	8	11	10	7	6	5	4	1	0	3	2	27	25	26	24	23	22	21	20	19	18	17	16	15	13	14	12
10	11	8	9	12	13	14	15	16	17	18	19	20	21	22	23	24	26	25	27	2	3	0	1	4	6	5	7
11	10	13	12	9	8	7	6	5	4	1	0	3	2	27	25	26	24	23	22	21	20	19	18	17	15	16	14
12	13	10	11	14	15	16	17	18	19	20	21	22	23	24	26	25	27	2	3	0	1	4	5	6	8	7	9
13	12	15	14	11	10	9	8	7	6	5	4	1	0	3	2	27	25	26	24	23	22	21	20	19	17	18	16
14	15	12	13	16	17	18	19	20	21	22	23	24	26	25	27	2	3	0	1	4	5	6	7	8	10	9	11
15	14	17	16	13	12	11	10	9	8	7	6	5	4	1	0	3	2	27	25	26	24	23	22	21	19	20	18
16	17	14	15	18	19	20	21	22	23	24	26	25	27	2	3	0	1	4	5	6	7	8	9	10	12	11	13
17	16	19	18	15	14	13	12	11	10	9	8	7	6	5	4	1	0	3	2	27	25	26	24	23	21	22	20
18	19	16	17	20	21	22	23	24	26	25	27	2	3	0	1	4	5	6	7	8	9	10	11	12	14	13	15
19	18	21	20	17	16	15	14	13	12	11	10	9	8	7	6	5	4	1	0	3	2	27	25	26	23	24	22
20	21	18	19	22	23	24	26	25	27	2	3	0	1	4	5	6	7	8	9	10	11	12	13	14	16	15	17
21	20	23	22	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	1	0	3	2	27	26	25	24
22	23	20	21	24	26	25	27	2	3	0	1	4	5	6	7	8	9	10	11	12	13	14	15	16	18	17	19
23	22	26	24	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	1	0	3	27	2	25
24	26	22	23	25	27	2	3	0	1	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	20	19	21
25	27	24	26	2	3	0	1	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	22	21	23
26	24	27	25	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	1	3	0	2
27	25	3	2	26	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	1	4	0

Centre: 0 16

Centrum: 0 16

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

15 Elements of order 2: 1 3 5 7 9 11 13 15 16 17 19 21 23 26 27

6 Elements of order 7: 6 10 14 18 22 25

6 Elements of order 14: 2 4 8 12 20 24

Commutator Subloop: 0 6 10 14 18 22 25

Associator Subloop: 0

2 Conjugacy Classes of size 1:

0
16

6 Conjugacy Classes of size 2:

2 4
6 25
8 24
10 22
12 20
14 18

2 Conjugacy Classes of size 7:

1 7 11 15 19 23 27
3 5 9 13 17 21 26

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