Right Bol Loop 20.15.1.0 of order 20

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
1	4	0	2	3	8	9	5	6	7	14	17	16	19	18	11	10	13	12	15
2	0	3	4	1	7	8	9	5	6	16	15	18	17	10	19	12	11	14	13
3	2	4	1	0	9	5	6	7	8	12	19	14	11	16	13	18	15	10	17
4	3	1	0	2	6	7	8	9	5	18	13	10	15	12	17	14	19	16	11
5	7	8	6	9	0	3	1	2	4	11	14	19	12	17	10	15	18	13	16
6	8	9	7	5	4	0	3	1	2	19	16	17	14	15	12	13	10	11	18
7	9	5	8	6	2	4	0	3	1	17	18	15	16	13	14	11	12	19	10
8	5	6	9	7	1	2	4	0	3	15	10	13	18	11	16	19	14	17	12
9	6	7	5	8	3	1	2	4	0	13	12	11	10	19	18	17	16	15	14
10	16	14	18	12	13	15	17	19	11	0	8	4	9	2	5	1	6	3	7
11	15	17	13	19	18	16	14	12	10	5	0	9	3	8	1	7	2	6	4
12	18	16	10	14	15	17	19	11	13	3	9	0	5	4	6	2	7	1	8
13	17	19	15	11	10	18	16	14	12	9	4	8	0	7	3	6	1	5	2
14	10	18	12	16	17	19	11	13	15	1	5	3	6	0	7	4	8	2	9
15	19	11	17	13	12	10	18	16	14	8	2	7	4	6	0	5	3	9	1
16	12	10	14	18	19	11	13	15	17	2	6	1	7	3	8	0	9	4	5
17	11	13	19	15	14	12	10	18	16	7	1	6	2	5	4	9	0	8	3
18	14	12	16	10	11	13	15	17	19	4	7	2	8	1	9	3	5	0	6
19	13	15	11	17	16	14	12	10	18	6	3	5	1	9	2	8	4	7	0

Centre: 0

Centrum: 0

Nucleus: 0

Left Nucleus: 0 9 16 17

Middle Nucleus: 0 1 2 3 4

Right Nucleus: 0 1 2 3 4

1 Element of order 1: 0

15 Elements of order 2: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

4 Elements of order 5: 1 2 3 4

Commutator Subloop: 0 1 2 3 4

Associator Subloop: 0 1 2 3 4

1 Conjugacy Class of size 1:

2 Conjugacy Classes of size 2:

3 Conjugacy Classes of size 5:

5 6 7 8 9
10 12 14 16 18
11 13 15 17 19

Automorphic Inverse Property: FAILS. (1^-1)(6^-1) neq (1*6)^-1

A_l Property: FAILS. The left inner mapping L_5,1 = (10,18,16,14,12)(11,13,15,17,19) is not an automorphism. L_5,1(10*5) neq L_5,1(10)*L_5,1(5)

A_r Property: HOLDS (i.e. every right inner mapping R_a,b is an automorphism)

Right (Left, Full) Mult Group Orders: 40 (2500, 5000)

/ revised November, 2001

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
1	4	0	2	3	8	9	5	6	7	14	17	16	19	18	11	10	13	12	15
2	0	3	4	1	7	8	9	5	6	16	15	18	17	10	19	12	11	14	13
3	2	4	1	0	9	5	6	7	8	12	19	14	11	16	13	18	15	10	17
4	3	1	0	2	6	7	8	9	5	18	13	10	15	12	17	14	19	16	11
5	7	8	6	9	0	3	1	2	4	11	14	19	12	17	10	15	18	13	16
6	8	9	7	5	4	0	3	1	2	19	16	17	14	15	12	13	10	11	18
7	9	5	8	6	2	4	0	3	1	17	18	15	16	13	14	11	12	19	10
8	5	6	9	7	1	2	4	0	3	15	10	13	18	11	16	19	14	17	12
9	6	7	5	8	3	1	2	4	0	13	12	11	10	19	18	17	16	15	14
10	16	14	18	12	13	15	17	19	11	0	8	4	9	2	5	1	6	3	7
11	15	17	13	19	18	16	14	12	10	5	0	9	3	8	1	7	2	6	4
12	18	16	10	14	15	17	19	11	13	3	9	0	5	4	6	2	7	1	8
13	17	19	15	11	10	18	16	14	12	9	4	8	0	7	3	6	1	5	2
14	10	18	12	16	17	19	11	13	15	1	5	3	6	0	7	4	8	2	9
15	19	11	17	13	12	10	18	16	14	8	2	7	4	6	0	5	3	9	1
16	12	10	14	18	19	11	13	15	17	2	6	1	7	3	8	0	9	4	5
17	11	13	19	15	14	12	10	18	16	7	1	6	2	5	4	9	0	8	3
18	14	12	16	10	11	13	15	17	19	4	7	2	8	1	9	3	5	0	6
19	13	15	11	17	16	14	12	10	18	6	3	5	1	9	2	8	4	7	0

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
1	4	0	2	3	8	9	5	6	7	14	17	16	19	18	11	10	13	12	15
2	0	3	4	1	7	8	9	5	6	16	15	18	17	10	19	12	11	14	13
3	2	4	1	0	9	5	6	7	8	12	19	14	11	16	13	18	15	10	17
4	3	1	0	2	6	7	8	9	5	18	13	10	15	12	17	14	19	16	11
5	7	8	6	9	0	3	1	2	4	11	14	19	12	17	10	15	18	13	16
6	8	9	7	5	4	0	3	1	2	19	16	17	14	15	12	13	10	11	18
7	9	5	8	6	2	4	0	3	1	17	18	15	16	13	14	11	12	19	10
8	5	6	9	7	1	2	4	0	3	15	10	13	18	11	16	19	14	17	12
9	6	7	5	8	3	1	2	4	0	13	12	11	10	19	18	17	16	15	14
10	16	14	18	12	13	15	17	19	11	0	8	4	9	2	5	1	6	3	7
11	15	17	13	19	18	16	14	12	10	5	0	9	3	8	1	7	2	6	4
12	18	16	10	14	15	17	19	11	13	3	9	0	5	4	6	2	7	1	8
13	17	19	15	11	10	18	16	14	12	9	4	8	0	7	3	6	1	5	2
14	10	18	12	16	17	19	11	13	15	1	5	3	6	0	7	4	8	2	9
15	19	11	17	13	12	10	18	16	14	8	2	7	4	6	0	5	3	9	1
16	12	10	14	18	19	11	13	15	17	2	6	1	7	3	8	0	9	4	5
17	11	13	19	15	14	12	10	18	16	7	1	6	2	5	4	9	0	8	3
18	14	12	16	10	11	13	15	17	19	4	7	2	8	1	9	3	5	0	6
19	13	15	11	17	16	14	12	10	18	6	3	5	1	9	2	8	4	7	0

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
1	4	0	2	3	8	9	5	6	7	14	17	16	19	18	11	10	13	12	15
2	0	3	4	1	7	8	9	5	6	16	15	18	17	10	19	12	11	14	13
3	2	4	1	0	9	5	6	7	8	12	19	14	11	16	13	18	15	10	17
4	3	1	0	2	6	7	8	9	5	18	13	10	15	12	17	14	19	16	11
5	7	8	6	9	0	3	1	2	4	11	14	19	12	17	10	15	18	13	16
6	8	9	7	5	4	0	3	1	2	19	16	17	14	15	12	13	10	11	18
7	9	5	8	6	2	4	0	3	1	17	18	15	16	13	14	11	12	19	10
8	5	6	9	7	1	2	4	0	3	15	10	13	18	11	16	19	14	17	12
9	6	7	5	8	3	1	2	4	0	13	12	11	10	19	18	17	16	15	14
10	16	14	18	12	13	15	17	19	11	0	8	4	9	2	5	1	6	3	7
11	15	17	13	19	18	16	14	12	10	5	0	9	3	8	1	7	2	6	4
12	18	16	10	14	15	17	19	11	13	3	9	0	5	4	6	2	7	1	8
13	17	19	15	11	10	18	16	14	12	9	4	8	0	7	3	6	1	5	2
14	10	18	12	16	17	19	11	13	15	1	5	3	6	0	7	4	8	2	9
15	19	11	17	13	12	10	18	16	14	8	2	7	4	6	0	5	3	9	1
16	12	10	14	18	19	11	13	15	17	2	6	1	7	3	8	0	9	4	5
17	11	13	19	15	14	12	10	18	16	7	1	6	2	5	4	9	0	8	3
18	14	12	16	10	11	13	15	17	19	4	7	2	8	1	9	3	5	0	6
19	13	15	11	17	16	14	12	10	18	6	3	5	1	9	2	8	4	7	0