Right Bol Loop 16.7.2.8 of order 16

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

Centre: 0 7

Centrum: 0 7

Nucleus: 0 7

Left Nucleus: 0 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

7 Elements of order 2: 7 8 9 11 13 14 15

4 Elements of order 4: 2 4 10 12

4 Elements of order 8: 1 3 5 6

Commutator Subloop: 0 2 4 7

Associator Subloop: 0 2 4 7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 3 5 6
8 11 13 14
9 10 12 15

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

A_l Property: FAILS. The left inner mapping L_1,1 = (8,13)(9,10)(11,14)(12,15) is not an automorphism. L_1,1(1*9) neq L_1,1(1)*L_1,1(9)

A_r Property: FAILS. The right inner mapping R_1,8 = (1,5)(2,4)(3,6)(8,11)(10,12)(13,14) is not an automorphism. R_1,8(1*8) neq R_1,8(1)*R_1,8(8)

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

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

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