Right Bol Loop 16.3.4.26 of order 16

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

Centre: 0 5

Centrum: 0 5 8 14

Nucleus: 0 5 9 15

Left Nucleus: 0 1 5 7 8 9 14 15

Middle Nucleus: 0 5 9 15

Right Nucleus: 0 5 9 15

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 5 7

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

Commutator Subloop: 0 5

Associator Subloop: 0 5

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

1 7
2 6
3 4
8 14
9 15
10 12
11 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: 32 (64, 128)

/ revised October, 2001

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

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

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