Right Bol Loop 16.1.2.32 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	11	10	13	12	15	14
2	3	1	0	6	7	11	10	4	5	8	9	14	15	12	13
3	2	0	1	7	6	10	11	5	4	9	8	15	14	13	12
4	5	6	7	1	0	12	13	3	2	14	15	8	9	10	11
5	4	7	6	0	1	13	12	2	3	15	14	9	8	11	10
6	7	5	4	3	2	1	0	14	15	13	12	11	10	9	8
7	6	4	5	2	3	0	1	15	14	12	13	10	11	8	9
8	9	10	11	12	13	15	14	1	0	3	2	5	4	6	7
9	8	11	10	13	12	14	15	0	1	2	3	4	5	7	6
10	11	9	8	15	14	2	3	12	13	1	0	6	7	5	4
11	10	8	9	14	15	3	2	13	12	0	1	7	6	4	5
12	13	15	14	9	8	5	4	11	10	6	7	1	0	3	2
13	12	14	15	8	9	4	5	10	11	7	6	0	1	2	3
14	15	12	13	10	11	8	9	7	6	5	4	3	2	1	0
15	14	13	12	11	10	9	8	6	7	4	5	2	3	0	1

Centre: 0 1

Centrum: 0 1

Nucleus: 0 1

Left Nucleus: 0 1 8 9

Middle Nucleus: 0 1

Right Nucleus: 0 1

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

1 Element of order 2: 1

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

Commutator Subloop: 0 1 14 15

Associator Subloop: 0 1 14 15

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

14 15

3 Conjugacy Classes of size 4:

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

Automorphic Inverse Property: FAILS. (2^-1)(5^-1) neq (2*5)^-1

A_l Property: FAILS. The left inner mapping L_2,2 = (4,10,5,11)(6,8,7,9)(12,13)(14,15) is not an automorphism. L_2,2(4*2) neq L_2,2(4)*L_2,2(2)

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

Right (Left, Full) Mult Group Orders: 64 (1024, 4096)

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

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

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