Right Bol Loop 16.3.2.12 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	15	13	11	14	12	10
2	3	4	1	6	7	0	5	11	12	13	8	10	9	15	14
3	2	7	4	5	0	1	6	12	11	14	10	15	8	9	13
4	7	6	5	0	3	2	1	15	10	9	14	13	12	11	8
5	6	1	0	3	4	7	2	13	14	11	9	8	15	10	12
6	5	0	7	2	1	4	3	14	13	12	15	9	10	8	11
7	4	5	2	1	6	3	0	10	15	8	12	14	11	13	9
8	10	11	12	15	13	14	9	4	7	1	6	3	5	2	0
9	15	12	14	10	11	13	8	7	4	0	3	2	6	5	1
10	8	13	11	9	14	12	15	1	0	4	5	6	2	3	7
11	13	15	9	14	10	8	12	6	5	3	4	7	1	0	2
12	14	10	15	13	8	9	11	5	6	2	1	4	0	7	3
13	11	9	8	12	15	10	14	3	2	6	7	0	4	1	5
14	12	8	10	11	9	15	13	2	3	5	0	1	7	4	6
15	9	14	13	8	12	11	10	0	1	7	2	5	3	6	4

Centre: 0 4

Centrum: 0 4

Nucleus: 0 4

Left Nucleus: 0 3 4 5

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 10
11 14
12 13

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