Right Bol Loop 16.7.2.166 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	15	13	12	11	10	8	14
2	4	0	1	6	7	3	5	10	12	15	8	9	14	13	11
3	5	1	7	0	6	2	4	12	11	9	14	15	8	10	13
4	2	6	0	7	1	5	3	13	10	14	9	8	15	11	12
5	3	7	6	1	0	4	2	11	13	8	15	14	9	12	10
6	7	4	2	5	3	0	1	14	8	12	13	10	11	15	9
7	6	5	4	3	2	1	0	15	14	11	10	13	12	9	8
8	9	11	13	12	10	14	15	7	1	5	2	3	4	6	0
9	8	13	10	11	12	15	14	6	7	3	4	5	2	0	1
10	13	15	14	9	8	12	11	5	3	0	7	1	6	4	2
11	12	8	9	14	15	13	10	2	4	7	0	6	1	3	5
12	11	14	8	15	9	10	13	4	5	6	1	7	0	2	3
13	10	9	15	8	14	11	12	3	2	1	6	0	7	5	4
14	15	12	11	10	13	8	9	1	0	4	3	2	5	7	6
15	14	10	12	13	11	9	8	0	6	2	5	4	3	1	7

Centre: 0 7

Centrum: 0 7

Nucleus: 0 7

Left Nucleus: 0 3 4 7

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

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

8 Elements of order 4: 3 4 8 9 12 13 14 15

Commutator Subloop: 0 7

Associator Subloop: 0 7

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

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

A_l Property: HOLDS (i.e. every left inner mapping L_a,b is an automorphism)

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

Right (Left, Full) Mult Group Orders: 64 (128, 512)

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