Right Bol Loop 16.9.2.383 of order 16

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

Centre: 0 15

Centrum: 0 15

Nucleus: 0 15

Left Nucleus: 0 15

Middle Nucleus: 0 15

Right Nucleus: 0 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

9 Elements of order 2: 1 3 5 7 9 10 13 14 15

6 Elements of order 4: 2 4 6 8 11 12

Commutator Subloop: 0 15

Associator Subloop: 0 15

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Automorphic Inverse Property: FAILS. (1^-1)(3^-1) neq (1*3)^-1

A_l Property: FAILS. The left inner mapping L_1,1 = (2,6)(3,5)(4,8)(9,14)(10,13)(11,12) is not an automorphism. L_1,1(2*3) neq L_1,1(2)*L_1,1(3)

A_r Property: HOLDS (i.e. every right inner mapping R_a,b is an automorphism)

Right (Left, Full) Mult Group Orders: 128 (1024, 2048)

/ revised October, 2001

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

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

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