Spin 3-blocks in covering groups of the symmetric and alternating groups:

Using spinsym package written by Lukas Maas.

Block information:

Defect.
k(B),l(B) invariants.
Core.
Decomposition Matrix sorted by number of prime parts.

Defect = 8

k(B) = 60, l(B) = 22

[ 19, 19, 20, 20, 22, 22, 26, 26, 26, 26, 164, 164, 166, 166, 377, 377, 418, 418, 522, 522, 1391, 1391 ]

2.Alt(18) 3-block 5, [ ]

k(B) = 60, l(B) = 11

[ 35, 36, 42, 50, 50, 324, 330, 753, 834, 1040, 2777 ]

2.Sym(18) 3-block 8, [ ]

Defect = 6

k(B) = 36, l(B) = 14

[ 8, 8, 16, 16, 26, 26, 26, 26, 60, 60, 140, 140, 190, 190 ]

2.Sym(15) 3-block 8, [ ]

[ 6, 6, 14, 14, 26, 26, 26, 26, 68, 68, 242, 242, 286, 286 ]

2.Sym(16) 3-block 9, [ 1 ]

[ 6, 6, 12, 12, 40, 40, 40, 40, 56, 56, 190, 190, 290, 290 ]

2.Alt(17) 3-block 6, [ 2 ]

k(B) = 36, l(B) = 7

[ 14, 30, 50, 50, 116, 279, 375 ]

2.Alt(15) 3-block 5, [ ]

[ 9, 24, 50, 50, 135, 483, 567 ]

2.Alt(16) 3-block 7, [ 1 ]

[ 9, 21, 77, 77, 111, 375, 579 ]

2.Sym(17) 3-block 9, [ 2 ]

Defect = 5

k(B) = 21, l(B) = 10

[ 10, 10, 11, 11, 13, 13, 13, 13, 82, 82 ]

2.Sym(17) 3-block 10, [ 4, 1 ]

[ 6, 6, 6, 6, 16, 16, 29, 29, 45, 45 ]

2.Alt(12) 3-block 5, [ ]

[ 3, 3, 16, 16, 17, 17, 21, 21, 53, 53 ]

2.Alt(13) 3-block 4, [ 1 ]

[ 3, 3, 13, 13, 13, 13, 21, 21, 69, 69 ]

2.Sym(14) 3-block 7, [ 2 ]

k(B) = 21, l(B) = 5

[ 18, 21, 25, 25, 162 ]

2.Alt(17) 3-block 7, [ 4, 1 ]

[ 10, 10, 30, 57, 87 ]

2.Sym(12) 3-block 8, [ ]

[ 3, 30, 33, 41, 105 ]

2.Sym(13) 3-block 6, [ 1 ]

[ 3, 25, 25, 39, 137 ]

2.Alt(14) 3-block 5, [ 2 ]

Defect = 4

k(B) = 12, l(B) = 6

[ 6, 6, 8, 8, 16, 16 ]

2.Sym(10) 3-block 6, [ 5, 2 ]
2.Alt(11) 3-block 4, [ 2 ]

[ 4, 4, 8, 8, 30, 30 ]

2.Alt(16) 3-block 8, [ 5, 2 ]
2.Alt(14) 3-block 6, [ 4, 1 ]

[ 4, 4, 6, 6, 14, 14 ]

2.Sym(9) 3-block 6, [ ]

k(B) = 12, l(B) = 3

[ 10, 15, 31 ]

2.Sym(11) 3-block 5, [ 2 ]
2.Alt(10) 3-block 4, [ 1 ]

[ 7, 15, 58 ]

2.Sym(16) 3-block 10, [ 5, 2 ]
2.Sym(14) 3-block 8, [ 4, 1 ]

[ 6, 10, 25 ]

2.Alt(9) 3-block 4, [ ]

Defect = 2

k(B) = 6, l(B) = 4

[ 3, 3, 5, 5 ]

2.Sym(8) 3-block 6, [ 2 ]
2.Alt(7) 3-block 3, [ 1 ]

[ 3, 3, 3, 3 ]

2.Sym(18) 3-block 9, [ 7, 4, 1 ]
2.Sym(13) 3-block 7, [ 5, 2 ]
2.Sym(11) 3-block 6, [ 4, 1 ]

[ 2, 2, 5, 5 ]

2.Alt(6) 3-block 3, [ ]

k(B) = 6, l(B) = 2

[ 5, 9 ]

2.Sym(7) 3-block 4, [ 1 ]
2.Alt(8) 3-block 6, [ 2 ]

[ 5, 5 ]

2.Alt(18) 3-block 6, [ 7, 4, 1 ]
2.Alt(13) 3-block 5, [ 5, 2 ]
2.Alt(11) 3-block 5, [ 4, 1 ]

[ 2, 9 ]

2.Sym(6) 3-block 4, [ ]

Defect = 1

k(B) = 3, l(B) = 2

[ 2, 2 ]

2.Sym(18) 3-block 10, [ 8, 5, 3, 2 ]
2.Alt(8) 3-block 5, [ 4, 1 ]
2.Alt(5) 3-block 4, [ 2 ]
2.Alt(15) 3-block 6, [ 7, 4, 1 ]
2.Alt(10) 3-block 5, [ 5, 2 ]

k(B) = 3, l(B) = 1

[ 3 ]

2.Sym(8) 3-block 5, [ 4, 1 ]
2.Sym(5) 3-block 4, [ 2 ]
2.Sym(15) 3-block 9, [ 7, 4, 1 ]
2.Sym(10) 3-block 7, [ 5, 2 ]
2.Alt(18) 3-block 7, [ 8, 5, 2 ]

Defect = 0

k(B) = 1, l(B) = 1

[ 1 ]

2.Sym(7) 3-block 6, [ 5, 2 ]
2.Sym(7) 3-block 5, [ 5, 2 ]
2.Sym(5) 3-block 6, [ 4, 1 ]
2.Sym(5) 3-block 5, [ 4, 1 ]
2.Sym(15) 3-block 10, [ 8, 5, 2 ]
2.Sym(12) 3-block 9, [ 7, 4, 1 ]
2.Sym(12) 3-block 10, [ 7, 4, 1 ]
2.Alt(7) 3-block 4, [ 5, 2 ]
2.Alt(5) 3-block 5, [ 4, 1 ]
2.Alt(15) 3-block 8, [ 8, 5, 2 ]
2.Alt(15) 3-block 7, [ 8, 5, 2 ]
2.Alt(12) 3-block 6, [ 7, 4, 1 ]

Last Update: November 18, 2012,using IndexOfSpinBlocks.gap, created by M.Schaps and GAP4, version 4.5; Aachen, St Andrews, 1999, http://www-gap.dcs.st-and.ac.u,/~gap