Right Bol Loop 16.9.2.336 of order 16

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

Centre: 0 10

Centrum: 0 10

Nucleus: 0 10

Left Nucleus: 0 10

Middle Nucleus: 0 10

Right Nucleus: 0 10

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

9 Elements of order 2: 5 8 9 10 11 12 13 14 15

6 Elements of order 4: 1 2 3 4 6 7

Commutator Subloop: 0 10

Associator Subloop: 0 10

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

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

A_l Property: FAILS. The left inner mapping L_1,1 = (2,4)(5,8)(6,7)(9,11)(12,14)(13,15) is not an automorphism. L_1,1(2*5) neq L_1,1(2)*L_1,1(5)

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

Right (Left, Full) Mult Group Orders: 128 (1024, 2048)

/ revised October, 2001

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

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

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