Ranks of B3(G)

These are some tables of ranks of B3(G) for:
1. G=Zn+Zn+Zn, n<=6;
2. G=Zn, n<=60;
3. G=Zn+Zm+Zr, n,m,r<=4.

[B3 for Groups of rank 3]
[ ZN+ZN+ZN,  Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 1, 1, 1, 1 ]
[ 2, 2, 2, 0, 8, 0, 0 ]
[ 3, 3, 3, 66, 66, 66, 66 ]
[ 4, 4, 4, 253, 281, 253, 253 ]
[ 5, 5, 5, 2606, 2606, 2606, 2732 ]
[ 6, 6, 6, 2458, 2550, 2550, 2458 ]





[B3 for cyclic Groups ]
[ ZN,  Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 1, 1, 1, 1 ]
[ 1, 1, 2, 0, 0, 0, 0 ]
[ 1, 1, 3, 0, 0, 0, 0 ]
[ 1, 1, 4, 0, 0, 0, 0 ]
[ 1, 1, 5, 0, 0, 0, 0 ]
[ 1, 1, 6, 0, 0, 0, 0 ]
[ 1, 1, 7, 0, 1, 0, 0 ]
[ 1, 1, 8, 0, 1, 0, 0 ]
[ 1, 1, 9, 1, 1, 1, 1 ]
[ 1, 1, 10, 0, 2, 0, 0 ]
[ 1, 1, 11, 1, 1, 1, 2 ]
[ 1, 1, 12, 2, 4, 2, 2 ]
[ 1, 1, 13, 2, 2, 2, 2 ]
[ 1, 1, 14, 1, 5, 1, 1 ]
[ 1, 1, 15, 5, 6, 5, 5 ]
[ 1, 1, 16, 3, 8, 3, 3 ]
[ 1, 1, 17, 5, 6, 6, 5 ]
[ 1, 1, 18, 5, 11, 5, 5 ]
[ 1, 1, 19, 7, 7, 8, 8 ]
[ 1, 1, 20, 7, 16, 7, 7 ]
[ 1, 1, 21, 11, 14, 11, 11 ]
[ 1, 1, 22, 7, 16, 7, 7 ]
[ 1, 1, 23, 12, 13, 12, 12 ]
[ 1, 1, 24, 13, 24, 13, 13 ]
[ 1, 1, 25, 16, 19, 16, 16 ]
[ 1, 1, 26, 12, 24, 12, 12 ]
[ 1, 1, 27, 21, 23, 22, 21 ]
[ 1, 1, 28, 17, 34, 17, 17 ]
[ 1, 1, 29, 22, 23, 22, 23 ]
[ 1, 1, 30, 22, 43, 23, 22 ]
[ 1, 1, 31, 26, 29, 26, 27 ]
[ 1, 1, 32, 24, 43, 24, 24 ]
[ 1, 1, 33, 34, 39, 34, 35 ]
[ 1, 1, 34, 26, 45, 26, 26 ]
[ 1, 1, 35, 37, 49, 37, 37 ]
[ 1, 1, 36, 38, 62, 39, 38 ]
[ 1, 1, 37, 40, 41, 41, 40 ]
[ 1, 1, 38, 35, 58, 35, 35 ]
[ 1, 1, 39, 51, 56, 51, 51 ]
[ 1, 1, 40, 44, 81, 45, 44 ]
[ 1, 1, 41, 51, 55, 51, 52 ]
[ 1, 1, 42, 51, 90, 52, 51 ]
[ 1, 1, 43, 58, 60, 58, 58 ]
[ 1, 1, 44, 55, 92, 55, 56 ]
[ 1, 1, 45, 76, 91, 78, 76 ]
[ 1, 1, 46, 57, 90, 57, 57 ]
[ 1, 1, 47, 70, 71, 70, 70 ]
[ 1, 1, 48, 76, 118, 76, 76 ]
[ 1, 1, 49, 78, 90, 78, 78 ]
[ 1, 1, 50, 72, 122, 74, 72 ]
[ 1, 1, 51, 97, 110, 98, 97 ]
[ 1, 1, 52, 84, 133, 84, 84 ]
[ 1, 1, 53, 92, 96, 93, 92 ]
[ 1, 1, 54, 95, 148, 97, 95 ]
[ 1, 1, 55, 107, 128, 107, 109 ]
[ 1, 1, 56, 98, 166, 99, 98 ]
[ 1, 1, 57, 124, 136, 125, 125 ]
[ 1, 1, 58, 100, 153, 100, 100 ]
[ 1, 1, 59, 118, 118, 118, 119 ]
[ 1, 1, 60, 138, 206, 140, 138 ]




[B3]
[ m, n, r, Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 1, 1, 1, 1 ]
[ 1, 1, 2, 0, 0, 0, 0 ]
[ 1, 1, 3, 0, 0, 0, 0 ]
[ 1, 1, 4, 0, 0, 0, 0 ]
[ 1, 2, 2, 0, 0, 0, 0 ]
[ 1, 2, 3, 0, 0, 0, 0 ]
[ 1, 2, 4, 0, 3, 0, 0 ]
[ 1, 3, 3, 3, 3, 3, 3 ]
[ 1, 3, 4, 2, 4, 2, 2 ]
[ 1, 4, 4, 5, 18, 5, 5 ]
[ 2, 2, 2, 0, 8, 0, 0 ]
[ 2, 2, 3, 0, 9, 0, 0 ]
[ 2, 2, 4, 0, 25, 0, 0 ]
[ 2, 3, 3, 10, 18, 10, 10 ]
[ 2, 3, 4, 9, 37, 9, 9 ]
[ 2, 4, 4, 20, 81, 20, 20 ]
[ 3, 3, 3, 66, 66, 66, 66 ]
[ 3, 3, 4, 53, 77, 53, 53 ]
[ 3, 4, 4, 81, 161, 81, 81 ]
[ 4, 4, 4, 253, 281, 253, 253 ]

Ranks of B3^-(G)

These are some tables of ranks of B_3^-(G) for:
1. G=Zn+Zn+Zn, n<=6
2. G=Zn, n<=60
3. G=Zn+Zm+Zr, n,m,r<=4

[B3^- for Groups of rank 3]
[ ZN+ZN+ZN,  Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 0, 1, 0, 0 ]
[ 2, 2, 2, 0, 8, 0, 0 ]
[ 3, 3, 3, 27, 27, 27, 27 ]
[ 4, 4, 4, 113, 113, 113, 113 ]
[ 5, 5, 5, 1242, 1242, 1242, 1242 ]
[ 6, 6, 6, 1275, 1276, 1275, 1275 ]




[B3^- for Cyclic Groups]
[ZN,  Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
...0
[ 1, 1, 8, 0, 1, 0, 0 ]
[ 1, 1, 9, 0, 0, 0, 0 ]
[ 1, 1, 10, 0, 2, 0, 0 ]
[ 1, 1, 11, 0, 1, 0, 0 ]
[ 1, 1, 12, 0, 3, 0, 0 ]
[ 1, 1, 13, 0, 2, 0, 0 ]
[ 1, 1, 14, 0, 5, 0, 0 ]
[ 1, 1, 15, 0, 3, 0, 0 ]
[ 1, 1, 16, 0, 7, 0, 0 ]
[ 1, 1, 17, 0, 5, 0, 0 ]
[ 1, 1, 18, 0, 9, 0, 0 ]
[ 1, 1, 19, 0, 7, 0, 0 ]
[ 1, 1, 20, 0, 13, 0, 0 ]
[ 1, 1, 21, 0, 9, 0, 0 ]
[ 1, 1, 22, 0, 16, 0, 0 ]
[ 1, 1, 23, 0, 12, 0, 0 ]
[ 1, 1, 24, 0, 18, 0, 0 ]
[ 1, 1, 25, 0, 16, 0, 0 ]
[ 1, 1, 26, 0, 24, 0, 0 ]
[ 1, 1, 27, 1, 18, 1, 1 ]
[ 1, 1, 28, 0, 29, 0, 0 ]
[ 1, 1, 29, 0, 23, 0, 0 ]
[ 1, 1, 30, 0, 33, 0, 0 ]
[ 1, 1, 31, 0, 26, 0, 0 ]
[ 1, 1, 32, 0, 38, 0, 0 ]
[ 1, 1, 33, 2, 31, 2, 2 ]
[ 1, 1, 34, 0, 45, 0, 0 ]
[ 1, 1, 35, 0, 39, 0, 0 ]
[ 1, 1, 36, 3, 49, 3, 3 ]
[ 1, 1, 37, 0, 41, 0, 0 ]
[ 1, 1, 38, 0, 58, 0, 0 ]
[ 1, 1, 39, 4, 47, 4, 4 ]
[ 1, 1, 40, 0, 66, 0, 0 ]
[ 1, 1, 41, 0, 54, 0, 0 ]
[ 1, 1, 42, 2, 73, 2, 2 ]
[ 1, 1, 43, 1, 58, 1, 1 ]
[ 1, 1, 44, 2, 82, 2, 2 ]
[ 1, 1, 45, 8, 69, 8, 8 ]
[ 1, 1, 46, 0, 90, 0, 0 ]
[ 1, 1, 47, 0, 70, 0, 0 ]
[ 1, 1, 48, 7, 94, 7, 7 ]
[ 1, 1, 49, 0, 81, 0, 0 ]
[ 1, 1, 50, 0, 110, 0, 0 ]
[ 1, 1, 51, 11, 93, 11, 11 ]
[ 1, 1, 52, 5, 120, 5, 5 ]
[ 1, 1, 53, 0, 96, 0, 0 ]
[ 1, 1, 54, 7, 127, 7, 7 ]
[ 1, 1, 55, 4, 111, 4, 4 ]
[ 1, 1, 56, 2, 141, 2, 2 ]
[ 1, 1, 57, 14, 118, 14, 14 ]
[ 1, 1, 58, 0, 153, 0, 0 ]
[ 1, 1, 59, 1, 118, 1, 1 ]
[ 1, 1, 60, 20, 159, 20, 20 ]




[B3^-]
[ m, n, r, Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 0, 1, 0, 0 ]
[ 1, 1, 2, 0, 0, 0, 0 ]
[ 1, 1, 3, 0, 0, 0, 0 ]
[ 1, 1, 4, 0, 0, 0, 0 ]
[ 1, 2, 2, 0, 0, 0, 0 ]
[ 1, 2, 3, 0, 0, 0, 0 ]
[ 1, 2, 4, 0, 3, 0, 0 ]
[ 1, 3, 3, 0, 0, 0, 0 ]
[ 1, 3, 4, 0, 3, 0, 0 ]
[ 1, 4, 4, 0, 12, 0, 0 ]
[ 2, 2, 2, 0, 8, 0, 0 ]
[ 2, 2, 3, 0, 7, 0, 0 ]
[ 2, 2, 4, 0, 17, 0, 0 ]
[ 2, 3, 3, 0, 10, 0, 0 ]
[ 2, 3, 4, 0, 26, 0, 0 ]
[ 2, 4, 4, 0, 41, 0, 0 ]
[ 3, 3, 3, 27, 27, 27, 27 ]
[ 3, 3, 4, 10, 46, 10, 10 ]
[ 3, 4, 4, 16, 104, 16, 16 ]
[ 4, 4, 4, 113, 113, 113, 113 ]

Ranks of M3(G)

These are some tables of ranks of M3(G) for:
1. G=Zn+Zn+Zn, n<=6
2. G=Zn, n<=60
3. G=Zn+Zm+Zr, n,m,r<=4


[M3 for Groups of rank 3]
[ ZN+ZN+ZN,  Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 0, 0, 0, 0 ]
[ 2, 2, 2, 0, 8, 0, 0 ]
[ 3, 3, 3, 66, 66, 66, 66 ]
[ 4, 4, 4, 253, 281, 253, 253 ]
[ 5, 5, 5, 2606, 2606, 2606, 2732 ]
[ 6, 6, 6, 2458, 2550, 2550, 2458 ]





[M3 for cyclic Groups]
[ ZN,  Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 0, 0, 0, 0 ]
[ 1, 1, 2, 0, 0, 0, 0 ]
[ 1, 1, 3, 0, 0, 0, 0 ]
[ 1, 1, 4, 0, 1, 0, 0 ]
[ 1, 1, 5, 0, 1, 0, 0 ]
[ 1, 1, 6, 0, 3, 0, 0 ]
[ 1, 1, 7, 0, 2, 0, 0 ]
[ 1, 1, 8, 0, 5, 0, 0 ]
[ 1, 1, 9, 1, 4, 1, 1 ]
[ 1, 1, 10, 0, 9, 0, 0 ]
[ 1, 1, 11, 1, 6, 1, 1 ]
[ 1, 1, 12, 2, 12, 2, 2 ]
[ 1, 1, 13, 2, 9, 2, 2 ]
[ 1, 1, 14, 1, 17, 1, 1 ]
[ 1, 1, 15, 5, 16, 5, 5 ]
[ 1, 1, 16, 3, 21, 3, 3 ]
[ 1, 1, 17, 5, 17, 5, 5 ]
[ 1, 1, 18, 5, 28, 5, 5 ]
[ 1, 1, 19, 7, 22, 7, 7 ]
[ 1, 1, 20, 7, 36, 7, 7 ]
[ 1, 1, 21, 11, 33, 11, 11 ]
[ 1, 1, 22, 7, 41, 7, 7 ]
[ 1, 1, 23, 12, 34, 12, 12 ]
[ 1, 1, 24, 13, 50, 13, 13 ]
[ 1, 1, 25, 16, 47, 16, 16 ]
[ 1, 1, 26, 12, 57, 12, 12 ]
[ 1, 1, 27, 21, 54, 22, 21 ]
[ 1, 1, 28, 17, 70, 17, 17 ]
[ 1, 1, 29, 22, 58, 22, 22 ]
[ 1, 1, 30, 22, 83, 23, 22 ]
[ 1, 1, 31, 26, 66, 26, 26 ]
[ 1, 1, 32, 24, 87, 24, 24 ]
[ 1, 1, 33, 34, 86, 34, 35 ]
[ 1, 1, 34, 26, 97, 26, 26 ]
[ 1, 1, 35, 37, 106, 37, 37 ]
[ 1, 1, 36, 38, 115, 39, 38 ]
[ 1, 1, 37, 40, 98, 40, 40 ]
[ 1, 1, 38, 35, 121, 35, 35 ]
[ 1, 1, 39, 51, 122, 51, 51 ]
[ 1, 1, 40, 44, 149, 45, 44 ]
[ 1, 1, 41, 51, 124, 51, 51 ]
[ 1, 1, 42, 51, 162, 52, 51 ]
[ 1, 1, 43, 58, 135, 58, 58 ]
[ 1, 1, 44, 55, 172, 55, 56 ]
[ 1, 1, 45, 76, 178, 78, 76 ]
[ 1, 1, 46, 57, 178, 57, 57 ]
[ 1, 1, 47, 70, 162, 70, 70 ]
[ 1, 1, 48, 76, 206, 76, 76 ]
[ 1, 1, 49, 78, 194, 78, 78 ]
[ 1, 1, 50, 72, 225, 74, 72 ]
[ 1, 1, 51, 97, 217, 98, 97 ]
[ 1, 1, 52, 84, 241, 84, 84 ]
[ 1, 1, 53, 92, 213, 92, 92 ]
[ 1, 1, 54, 95, 259, 97, 95 ]
[ 1, 1, 55, 107, 266, 107, 109 ]
[ 1, 1, 56, 98, 292, 99, 98 ]
[ 1, 1, 57, 124, 271, 125, 125 ]
[ 1, 1, 58, 100, 286, 100, 100 ]
[ 1, 1, 59, 118, 263, 118, 118 ]
[ 1, 1, 60, 138, 338, 140, 138 ]



[M3]
[ m, n, r, Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 0, 0, 0, 0 ]
[ 1, 1, 2, 0, 0, 0, 0 ]
[ 1, 1, 3, 0, 0, 0, 0 ]
[ 1, 1, 4, 0, 1, 0, 0 ]
[ 1, 2, 2, 0, 2, 0, 0 ]
[ 1, 2, 3, 0, 3, 0, 0 ]
[ 1, 2, 4, 0, 8, 0, 0 ]
[ 1, 3, 3, 3, 7, 3, 3 ]
[ 1, 3, 4, 2, 12, 2, 2 ]
[ 1, 4, 4, 5, 30, 5, 5 ]
[ 2, 2, 2, 0, 8, 0, 0 ]
[ 2, 2, 3, 0, 17, 0, 0 ]
[ 2, 2, 4, 0, 25, 0, 0 ]
[ 2, 3, 3, 10, 33, 10, 10 ]
[ 2, 3, 4, 9, 57, 9, 9 ]
[ 2, 4, 4, 20, 81, 20, 20 ]
[ 3, 3, 3, 66, 66, 66, 66 ]
[ 3, 3, 4, 53, 123, 53, 53 ]
[ 3, 4, 4, 81, 219, 81, 81 ]
[ 4, 4, 4, 253, 281, 253, 253 ]

Ranks of M3^-(G)

These are some tables of ranks of M_3^-(G) for:
1. G=Zn+Zn+Zn, n<=6
2. G=Zn, n<=60
3. G=Zn+Zm+Zr, n,m,r<=6



[M3^- for Groups of rank 3]
[ ZN+ZN+ZN,  Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 0, 0, 0, 0 ]
[ 2, 2, 2, 0, 8, 0, 0 ]
[ 3, 3, 3, 27, 27, 27, 27 ]
[ 4, 4, 4, 113, 113, 113, 113 ]
[ 5, 5, 5, 1242, 1242, 1242, 1242 ]
[ 6, 6, 6, 1275, 1276, 1275, 1275 ]





[M3^- for Cyclic Groups]
[ZN,  Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 0, 0, 0, 0 ]
[ 1, 1, 2, 0, 0, 0, 0 ]
[ 1, 1, 3, 0, 0, 0, 0 ]
[ 1, 1, 4, 0, 1, 0, 0 ]
[ 1, 1, 5, 0, 1, 0, 0 ]
[ 1, 1, 6, 0, 2, 0, 0 ]
[ 1, 1, 7, 0, 2, 0, 0 ]
[ 1, 1, 8, 0, 4, 0, 0 ]
[ 1, 1, 9, 0, 3, 0, 0 ]
[ 1, 1, 10, 0, 7, 0, 0 ]
[ 1, 1, 11, 0, 6, 0, 0 ]
[ 1, 1, 12, 0, 8, 0, 0 ]
[ 1, 1, 13, 0, 9, 0, 0 ]
[ 1, 1, 14, 0, 14, 0, 0 ]
[ 1, 1, 15, 0, 11, 0, 0 ]
[ 1, 1, 16, 0, 17, 0, 0 ]
[ 1, 1, 17, 0, 17, 0, 0 ]
[ 1, 1, 18, 0, 21, 0, 0 ]
[ 1, 1, 19, 0, 22, 0, 0 ]
[ 1, 1, 20, 0, 27, 0, 0 ]
[ 1, 1, 21, 0, 25, 0, 0 ]
[ 1, 1, 22, 0, 36, 0, 0 ]
[ 1, 1, 23, 0, 34, 0, 0 ]
[ 1, 1, 24, 0, 36, 0, 0 ]
[ 1, 1, 25, 0, 41, 0, 0 ]
[ 1, 1, 26, 0, 51, 0, 0 ]
[ 1, 1, 27, 1, 45, 1, 1 ]
[ 1, 1, 28, 0, 56, 0, 0 ]
[ 1, 1, 29, 0, 58, 0, 0 ]
[ 1, 1, 30, 0, 61, 0, 0 ]
[ 1, 1, 31, 0, 66, 0, 0 ]
[ 1, 1, 32, 0, 74, 0, 0 ]
[ 1, 1, 33, 2, 71, 2, 2 ]
[ 1, 1, 34, 0, 89, 0, 0 ]
[ 1, 1, 35, 0, 87, 0, 0 ]
[ 1, 1, 36, 3, 88, 3, 3 ]
[ 1, 1, 37, 0, 98, 0, 0 ]
[ 1, 1, 38, 0, 112, 0, 0 ]
[ 1, 1, 39, 4, 103, 4, 4 ]
[ 1, 1, 40, 0, 118, 0, 0 ]
[ 1, 1, 41, 0, 124, 0, 0 ]
[ 1, 1, 42, 2, 127, 2, 2 ]
[ 1, 1, 43, 1, 135, 1, 1 ]
[ 1, 1, 44, 2, 147, 2, 2 ]
[ 1, 1, 45, 8, 141, 8, 8 ]
[ 1, 1, 46, 0, 167, 0, 0 ]
[ 1, 1, 47, 0, 162, 0, 0 ]
[ 1, 1, 48, 7, 162, 7, 7 ]
[ 1, 1, 49, 0, 179, 0, 0 ]
[ 1, 1, 50, 0, 195, 0, 0 ]
[ 1, 1, 51, 11, 189, 11, 11 ]
[ 1, 1, 52, 5, 210, 5, 5 ]
[ 1, 1, 53, 0, 213, 0, 0 ]
[ 1, 1, 54, 7, 217, 7, 7 ]
[ 1, 1, 55, 4, 231, 4, 4 ]
[ 1, 1, 56, 2, 243, 2, 2 ]
[ 1, 1, 57, 14, 238, 14, 14 ]
[ 1, 1, 58, 0, 272, 0, 0 ]
[ 1, 1, 59, 1, 263, 1, 1 ]
[ 1, 1, 60, 20, 259, 20, 20 ]








[M3^- for Zn+Zm+Zr]
[ m, n, r, Q-rank,Fq-rank...]
[ 0, 0, 0, 0, 2, 3, 5 ]
[ 1, 1, 1, 0, 0, 0, 0 ]
[ 1, 1, 2, 0, 0, 0, 0 ]
[ 1, 1, 3, 0, 0, 0, 0 ]
[ 1, 1, 4, 0, 1, 0, 0 ]
[ 1, 2, 2, 0, 2, 0, 0 ]
[ 1, 2, 3, 0, 2, 0, 0 ]
[ 1, 2, 4, 0, 6, 0, 0 ]
[ 1, 3, 3, 0, 3, 0, 0 ]
[ 1, 3, 4, 0, 8, 0, 0 ]
[ 1, 4, 4, 0, 17, 0, 0 ]
[ 2, 2, 2, 0, 8, 0, 0 ]
[ 2, 2, 3, 0, 12, 0, 0 ]
[ 2, 2, 4, 0, 17, 0, 0 ]
[ 2, 3, 3, 0, 17, 0, 0 ]
[ 2, 3, 4, 0, 38, 0, 0 ]
[ 2, 4, 4, 0, 41, 0, 0 ]
[ 3, 3, 3, 27, 27, 27, 27 ]
[ 3, 3, 4, 10, 71, 10, 10 ]
[ 3, 4, 4, 16, 137, 16, 16 ]
[ 4, 4, 4, 113, 113, 113, 113 ]