Right Bol Loop 16.15.2.1 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	12	11	14	15	10	13	8
2	3	0	1	5	4	7	6	10	11	8	9	14	15	12	13
3	2	1	0	7	6	5	4	11	14	9	12	13	8	15	10
4	6	5	7	0	2	1	3	13	10	15	8	11	12	9	14
5	7	4	6	2	0	3	1	15	8	13	10	9	14	11	12
6	4	7	5	1	3	0	2	14	13	12	15	10	9	8	11
7	5	6	4	3	1	2	0	12	15	14	13	8	11	10	9
8	9	12	11	13	15	14	10	0	5	2	4	7	3	6	1
9	8	15	10	14	12	13	11	1	0	3	2	5	6	4	7
10	11	14	9	15	13	12	8	2	4	0	5	6	1	7	3
11	10	13	8	12	14	15	9	3	2	1	0	4	7	5	6
12	15	8	13	11	9	10	14	7	1	6	3	0	4	2	5
13	14	11	12	8	10	9	15	4	6	5	7	3	0	1	2
14	13	10	15	9	11	8	12	6	3	7	1	2	5	0	4
15	12	9	14	10	8	11	13	5	7	4	6	1	2	3	0

Centre: 0 6

Centrum: 0 6

Nucleus: 0 6

Left Nucleus: 0 2 6 7

Middle Nucleus: 0 6

Right Nucleus: 0 6

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

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

Commutator Subloop: 0 2 6 7

Associator Subloop: 0 2 6 7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 3 4 5
8 10 12 14
9 11 13 15

Automorphic Inverse Property: HOLDS

A_l Property: FAILS. The left inner mapping L_1,8 = (2,7)(3,5)(8,12)(9,15)(10,14)(11,13) is not an automorphism. L_1,8(2*8) neq L_1,8(2)*L_1,8(8)

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

Right (Left, Full) Mult Group Orders: 64 (4096, 16384)

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

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

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