Right Bol Loop 16.7.4.3 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	8	11	10	15	14	13	12
2	3	0	1	5	4	7	6	10	11	8	9	13	12	15	14
3	2	1	0	7	6	5	4	11	10	9	8	14	15	12	13
4	6	5	7	0	2	1	3	15	12	14	13	9	11	10	8
5	7	4	6	2	0	3	1	14	13	15	12	11	9	8	10
6	4	7	5	1	3	0	2	12	15	13	14	8	10	11	9
7	5	6	4	3	1	2	0	13	14	12	15	10	8	9	11
8	12	10	13	15	14	11	9	4	7	5	6	3	1	2	0
9	15	11	14	12	13	10	8	6	5	7	4	2	0	3	1
10	13	8	12	14	15	9	11	5	6	4	7	1	3	0	2
11	14	9	15	13	12	8	10	7	4	6	5	0	2	1	3
12	8	13	10	9	11	14	15	1	2	3	0	5	4	7	6
13	10	12	8	11	9	15	14	3	0	1	2	4	5	6	7
14	11	15	9	10	8	12	13	2	1	0	3	6	7	4	5
15	9	14	11	8	10	13	12	0	3	2	1	7	6	5	4

Centre: 0 2

Centrum: 0 2 4 5

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: 1 2 3 4 5 6 7

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

Commutator Subloop: 0 2 4 5

Associator Subloop: 0 2 4 5

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 3 6 7
8 10 14 15
9 11 12 13

Automorphic Inverse Property: FAILS. (1^-1)(9^-1) neq (1*9)^-1

A_l Property: FAILS. The left inner mapping L_1,8 = (4,5)(6,7)(8,14)(9,13)(10,15)(11,12) 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	0	3	2	6	7	4	5	9	8	11	10	15	14	13	12
2	3	0	1	5	4	7	6	10	11	8	9	13	12	15	14
3	2	1	0	7	6	5	4	11	10	9	8	14	15	12	13
4	6	5	7	0	2	1	3	15	12	14	13	9	11	10	8
5	7	4	6	2	0	3	1	14	13	15	12	11	9	8	10
6	4	7	5	1	3	0	2	12	15	13	14	8	10	11	9
7	5	6	4	3	1	2	0	13	14	12	15	10	8	9	11
8	12	10	13	15	14	11	9	4	7	5	6	3	1	2	0
9	15	11	14	12	13	10	8	6	5	7	4	2	0	3	1
10	13	8	12	14	15	9	11	5	6	4	7	1	3	0	2
11	14	9	15	13	12	8	10	7	4	6	5	0	2	1	3
12	8	13	10	9	11	14	15	1	2	3	0	5	4	7	6
13	10	12	8	11	9	15	14	3	0	1	2	4	5	6	7
14	11	15	9	10	8	12	13	2	1	0	3	6	7	4	5
15	9	14	11	8	10	13	12	0	3	2	1	7	6	5	4

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

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