Right Bol Loop 16.5.2.78 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	8	14	12	15	11	10	13
2	4	0	1	6	7	3	5	11	12	13	14	9	10	15	8
3	5	1	7	0	6	2	4	12	11	15	10	14	8	13	9
4	2	6	0	7	1	5	3	13	15	11	9	8	14	12	10
5	3	7	6	1	0	4	2	15	13	12	8	10	9	11	14
6	7	4	2	5	3	0	1	10	14	8	13	11	15	9	12
7	6	5	4	3	2	1	0	14	10	9	15	13	12	8	11
8	10	11	13	12	15	9	14	7	6	1	2	3	4	0	5
9	14	12	11	15	13	8	10	6	7	0	3	5	2	1	4
10	8	13	15	11	12	14	9	1	0	7	4	2	5	6	3
11	12	8	10	9	14	13	15	5	4	3	7	1	6	2	0
12	11	9	8	14	10	15	13	4	5	2	6	7	0	3	1
13	15	10	14	8	9	11	12	3	2	5	1	0	7	4	6
14	9	15	12	13	11	10	8	0	1	6	5	4	3	7	2
15	13	14	9	10	8	12	11	2	3	4	0	6	1	5	7

Centre: 0 7

Centrum: 0 7

Nucleus: 0 7

Left Nucleus: 0 7 12 13

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

5 Elements of order 2: 1 2 5 6 7

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