Right Bol Loop 16.9.2.321 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	15	14	13	12	11	10
2	4	0	6	1	7	3	5	11	14	13	8	15	10	9	12
3	5	1	7	0	6	2	4	13	12	11	10	9	8	15	14
4	2	6	0	7	1	5	3	14	11	12	9	10	15	8	13
5	3	7	1	6	0	4	2	12	13	14	15	8	9	10	11
6	7	4	5	2	3	0	1	10	15	8	13	14	11	12	9
7	6	5	4	3	2	1	0	15	10	9	12	11	14	13	8
8	10	12	13	14	11	9	15	7	1	6	5	2	3	4	0
9	15	14	11	12	13	8	10	6	0	7	3	4	5	2	1
10	8	13	12	11	14	15	9	1	7	0	4	3	2	5	6
11	13	15	10	9	8	14	12	5	4	3	7	0	6	1	2
12	14	8	9	10	15	13	11	2	3	4	0	7	1	6	5
13	11	10	15	8	9	12	14	4	5	2	1	6	0	7	3
14	12	9	8	15	10	11	13	3	2	5	6	1	7	0	4
15	9	11	14	13	12	10	8	0	6	1	2	5	4	3	7

Centre: 0 7

Centrum: 0 7

Nucleus: 0 7

Left Nucleus: 0 2 5 7 9 10 13 14

Middle Nucleus: 0 1 6 7

Right Nucleus: 0 1 6 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 13 14

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

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