Right Bol Loop 16.9.4.3 of order 16

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

Associator Subloop: 0 9 13 14

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

9 14

3 Conjugacy Classes of size 4:

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

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)(3,6)(4,5)(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: FAILS. The right inner mapping R_1,3 = (1,7)(2,8)(3,4)(5,6)(10,12)(11,15) is not an automorphism. R_1,3(1*1) neq R_1,3(1)*R_1,3(1)

Right (Left, Full) Mult Group Orders: 64 (1024, 4096)

/ revised October, 2001

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

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

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