Right Bol Loop 16.9.2.5 of order 16

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

Centre: 0 7

Centrum: 0 7

Nucleus: 0 7

Left Nucleus: 0 7 13 14

Middle Nucleus: 0 7

Right Nucleus: 0 7

Comm(L): This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.

1 Element of order 1: 0

9 Elements of order 2: 1 2 5 6 7 9 10 11 12

6 Elements of order 4: 3 4 8 13 14 15

Commutator Subloop: 0 3 4 7

Associator Subloop: 0 3 4 7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 2 5 6
8 13 14 15
9 10 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 = (2,5)(3,4)(8,13,15,14)(9,11,12,10) is not an automorphism. L_1,1(2*8) neq L_1,1(2)*L_1,1(8)

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

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

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

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