Right Bol Loop 16.3.2.73 of order 16

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

Centre: 0 4

Centrum: 0 4

Nucleus: 0 4

Left Nucleus: 0 4 9 14

Middle Nucleus: 0 4

Right Nucleus: 0 4

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

3 Elements of order 2: 1 4 7

12 Elements of order 4: 2 3 5 6 8 9 10 11 12 13 14 15

Commutator Subloop: 0 4

Associator Subloop: 0 4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Automorphic Inverse Property: FAILS. (2^-1)(9^-1) neq (2*9)^-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	6	7	2	5	4	9	8	11	13	10	12	15	14
2	3	4	1	6	7	0	5	10	12	8	9	14	15	11	13
3	2	7	4	5	0	1	6	11	13	9	15	8	14	10	12
4	7	6	5	0	3	2	1	15	14	13	12	11	10	9	8
5	6	1	0	3	4	7	2	12	10	14	8	15	9	13	11
6	5	0	7	2	1	4	3	13	11	15	14	9	8	12	10
7	4	5	2	1	6	3	0	14	15	12	10	13	11	8	9
8	9	10	12	15	11	13	14	4	7	6	3	5	2	1	0
9	8	11	10	14	13	12	15	7	4	5	6	2	3	0	1
10	11	15	14	13	9	8	12	6	3	4	1	7	0	5	2
11	10	14	8	12	15	9	13	5	2	7	4	0	1	6	3
12	13	9	15	11	8	14	10	3	6	1	0	4	7	2	5
13	12	8	9	10	14	15	11	2	5	0	7	1	4	3	6
14	15	12	13	9	10	11	8	1	0	3	2	6	5	4	7
15	14	13	11	8	12	10	9	0	1	2	5	3	6	7	4

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

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