Right Bol Loop 16.7.2.0 of order 16

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

Centre: 0 2

Centrum: 0 2

Nucleus: 0 2

Left Nucleus: 0 1 2 3 4 5 6 7

Middle Nucleus: 0 2

Right Nucleus: 0 2

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

7 Elements of order 2: 2 6 7 9 10 12 13

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

Automorphic Inverse Property: HOLDS

A_l Property: FAILS. The left inner mapping L_1,8 = (4,5)(6,7)(8,14)(9,12)(10,13)(11,15) is not an automorphism. L_1,8(4*8) neq L_1,8(4)*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 (1024, 4096)

/ revised October, 2001

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

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

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