Right Bol Loop 16.5.2.245 of order 16

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

Centre: 0 5

Centrum: 0 5

Nucleus: 0 5

Left Nucleus: 0 5 11 13

Middle Nucleus: 0 5

Right Nucleus: 0 5

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 3 4 5 7

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

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

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