Right Bol Loop 16.9.4.51 of order 16

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

Centre: 0 13

Centrum: 0 9 13 14

Nucleus: 0 13

Left Nucleus: 0 9 13 14

Middle Nucleus: 0 13

Right Nucleus: 0 13

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: 1 8 9 10 11 12 13 14 15

6 Elements of order 4: 2 3 4 5 6 7

Commutator Subloop: 0 13

Associator Subloop: 0 13

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

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

A_l Property: FAILS. The left inner mapping L_1,1 = (2,7)(3,5)(4,6)(9,14)(10,15)(11,12) is not an automorphism. L_1,1(2*3) neq L_1,1(2)*L_1,1(3)

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

Right (Left, Full) Mult Group Orders: 64 (1024, 2048)

/ revised October, 2001

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

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

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