Right Bol Loop 16.5.2.285 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	15	14	13	12
2	4	0	6	1	7	3	5	10	11	14	13	9	12	15	8
3	5	1	7	0	6	2	4	11	10	13	14	8	15	12	9
4	2	6	0	7	1	5	3	12	15	9	8	14	10	11	13
5	3	7	1	6	0	4	2	15	12	8	9	13	11	10	14
6	7	4	5	2	3	0	1	13	14	12	15	10	8	9	11
7	6	5	4	3	2	1	0	14	13	15	12	11	9	8	10
8	10	9	11	12	13	15	14	7	6	2	3	4	1	0	5
9	11	8	10	15	14	12	13	6	7	3	2	5	0	1	4
10	8	12	13	9	11	14	15	5	4	7	6	1	3	2	0
11	9	15	14	8	10	13	12	4	5	6	7	0	2	3	1
12	13	10	8	14	15	9	11	3	2	1	0	7	5	4	6
13	12	14	15	10	8	11	9	1	0	4	5	2	7	6	3
14	15	13	12	11	9	10	8	0	1	5	4	3	6	7	2
15	14	11	9	13	12	8	10	2	3	0	1	6	4	5	7

Centre: 0 7

Centrum: 0 7

Nucleus: 0 7

Left Nucleus: 0 1 6 7

Middle Nucleus: 0 7

Right Nucleus: 0 7

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

5 Elements of order 2: 1 2 5 6 7

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

Commutator Subloop: 0 3 4 7

Associator Subloop: 0 3 4 7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 2 5 6
8 11 12 14
9 10 13 15

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

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

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

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