Right Bol Loop 16.9.2.56 of order 16

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

Centre: 0 7

Centrum: 0 7

Nucleus: 0 7

Left Nucleus: 0 1 6 7 10 11 12 15

Middle Nucleus: 0 2 5 7

Right Nucleus: 0 2 5 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 11 12 13

6 Elements of order 4: 3 4 8 10 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 14
9 13
10 15
11 12

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: 32 (64, 256)

/ revised October, 2001

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

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

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