Right Bol Loop 16.11.6.2 of order 16

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

Centre: 0 2

Centrum: 0 1 2 3 4 7

Nucleus: 0 2

Left Nucleus: 0 1 2 3 4 5 6 7

Middle Nucleus: 0 2

Right Nucleus: 0 2

Comm(L): This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.

1 Element of order 1: 0

11 Elements of order 2: 2 4 7 8 9 10 11 12 13 14 15

4 Elements of order 4: 1 3 5 6

Commutator Subloop: 0 2

Associator Subloop: 0 2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

1 3
4 7
5 6
8 11
9 10
12 14
13 15

Automorphic Inverse Property: FAILS. (1^-1)(9^-1) neq (1*9)^-1

A_l Property: FAILS. The left inner mapping L_1,8 = (4,7)(5,6)(8,11)(9,10)(12,14)(13,15) is not an automorphism. L_1,8(4*8) neq L_1,8(4)*L_1,8(8)

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

Right (Left, Full) Mult Group Orders: 32 (1024, 2048)

/ revised October, 2001

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

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

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