Spin 5-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 = 3

k(B) = 30, l(B) = 20

[ 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 12, 12, 14, 14, 16, 16, 42, 42 ]

2.Sym(18) 5-block 38, [ 3 ]
2.Alt(17) 5-block 18, [ 2 ]

[ 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 10, 14, 14, 16, 16, 20, 20 ]

2.Alt(18) 5-block 20, [ 2, 1 ]

[ 4, 4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 10, 10, 20, 20, 26, 26 ]

2.Sym(15) 5-block 27, [ ]

[ 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8, 16, 16, 16, 16, 20, 20, 28, 28 ]

2.Sym(16) 5-block 30, [ 1 ]

k(B) = 27, l(B) = 10

[ 6, 6, 10, 10, 12, 12, 12, 18, 39, 49 ]

2.Alt(15) 5-block 16, [ 1 ]

[ 6, 6, 9, 9, 10, 12, 22, 27, 31, 83 ]

2.Sym(17) 5-block 28, [ 2 ]
2.Alt(18) 5-block 21, [ 3 ]

[ 4, 10, 10, 12, 12, 18, 19, 26, 30, 39 ]

2.Sym(18) 5-block 37, [ 2, 1 ]

[ 4, 6, 6, 9, 10, 12, 29, 31, 39, 55 ]

2.Alt(16) 5-block 19, [ 1 ]

Defect = 2

k(B) = 13, l(B) = 10

[ 3, 3, 4, 4, 4, 4, 4, 4, 5, 5 ]

2.Sym(17) 5-block 29, [ 4, 3 ]
2.Sym(13) 5-block 18, [ 2, 1 ]
2.Alt(16) 5-block 20, [ 4, 2 ]
2.Alt(14) 5-block 13, [ 3, 1 ]

[ 3, 3, 3, 3, 4, 4, 5, 5, 7, 7 ]

2.Sym(12) 5-block 20, [ 2 ]
2.Alt(13) 5-block 10, [ 3 ]

[ 2, 2, 4, 4, 4, 4, 5, 5, 5, 5 ]

2.Alt(10) 5-block 9, [ ]

[ 2, 2, 3, 3, 5, 5, 5, 5, 5, 5 ]

2.Alt(11) 5-block 8, [ 1 ]

[ 2, 2, 3, 3, 4, 4, 5, 5, 7, 7 ]

2.Sym(17) 5-block 27, [ 6, 1 ]

[ 2, 2, 3, 3, 3, 3, 6, 6, 9, 9 ]

2.Sym(14) 5-block 21, [ 4 ]

k(B) = 11, l(B) = 5

[ 5, 6, 6, 6, 9 ]

2.Sym(16) 5-block 31, [ 4, 2 ]
2.Sym(14) 5-block 22, [ 3, 1 ]
2.Alt(17) 5-block 19, [ 4, 3 ]
2.Alt(13) 5-block 11, [ 2, 1 ]

[ 3, 3, 6, 9, 13 ]

2.Sym(13) 5-block 17, [ 3 ]
2.Alt(12) 5-block 14, [ 2 ]

[ 2, 5, 6, 9, 13 ]

2.Alt(17) 5-block 17, [ 6, 1 ]

[ 2, 4, 6, 9, 9 ]

2.Sym(10) 5-block 16, [ ]

[ 2, 3, 7, 9, 9 ]

2.Sym(11) 5-block 14, [ 1 ]

[ 2, 3, 5, 10, 17 ]

2.Alt(14) 5-block 12, [ 4 ]

Defect = 1

k(B) = 5, l(B) = 4

[ 2, 2, 2, 2 ]

2.Sym(9) 5-block 12, [ 3, 1 ]
2.Sym(8) 5-block 11, [ 3 ]
2.Sym(6) 5-block 8, [ 1 ]
2.Sym(5) 5-block 4, [ ]
2.Sym(18) 5-block 39, [ 7, 4, 2 ]
2.Sym(14) 5-block 23, [ 6, 2, 1 ]
2.Sym(11) 5-block 15, [ 4, 2 ]
2.Alt(9) 5-block 8, [ 4 ]
2.Alt(8) 5-block 9, [ 2, 1 ]
2.Alt(7) 5-block 6, [ 2 ]
2.Alt(18) 5-block 25, [ 9, 4 ]
2.Alt(17) 5-block 20, [ 8, 3, 1 ]
2.Alt(16) 5-block 23, [ 8, 3 ]
2.Alt(15) 5-block 18, [ 7, 2, 1 ]
2.Alt(15) 5-block 17, [ 6, 3, 1 ]
2.Alt(14) 5-block 15, [ 7, 2 ]
2.Alt(12) 5-block 16, [ 6, 1 ]
2.Alt(12) 5-block 15, [ 4, 3 ]

k(B) = 4, l(B) = 2

[ 3, 3 ]

2.Sym(9) 5-block 11, [ 4 ]
2.Sym(7) 5-block 8, [ 2 ]
2.Sym(18) 5-block 41, [ 9, 4 ]
2.Sym(16) 5-block 33, [ 8, 3 ]
2.Sym(14) 5-block 24, [ 7, 2 ]
2.Sym(12) 5-block 22, [ 6, 1 ]
2.Alt(8) 5-block 8, [ 3 ]
2.Alt(6) 5-block 5, [ 1 ]

[ 2, 3 ]

2.Sym(8) 5-block 12, [ 2, 1 ]
2.Sym(17) 5-block 30, [ 8, 3, 1 ]
2.Sym(15) 5-block 29, [ 7, 2, 1 ]
2.Sym(15) 5-block 28, [ 6, 3, 1 ]
2.Sym(12) 5-block 21, [ 4, 3 ]
2.Alt(9) 5-block 9, [ 3, 1 ]
2.Alt(5) 5-block 3, [ ]
2.Alt(18) 5-block 22, [ 7, 4, 2 ]
2.Alt(14) 5-block 14, [ 6, 2, 1 ]
2.Alt(11) 5-block 9, [ 4, 2 ]

Defect = 0

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

[ 1 ]

2.Sym(9) 5-block 15, [ 7, 2 ]
2.Sym(9) 5-block 14, [ 7, 2 ]
2.Sym(9) 5-block 13, [ 6, 2, 1 ]
2.Sym(7) 5-block 9, [ 4, 3 ]
2.Sym(7) 5-block 12, [ 6, 1 ]
2.Sym(7) 5-block 11, [ 6, 1 ]
2.Sym(7) 5-block 10, [ 4, 3 ]
2.Sym(6) 5-block 9, [ 4, 2 ]
2.Sym(18) 5-block 43, [ 11, 6, 1 ]
2.Sym(18) 5-block 42, [ 11, 6, 1 ]
2.Sym(18) 5-block 40, [ 8, 6, 3, 1 ]
2.Sym(16) 5-block 35, [ 9, 4, 3 ]
2.Sym(16) 5-block 34, [ 9, 4, 3 ]
2.Sym(16) 5-block 32, [ 7, 6, 2, 1 ]
2.Sym(15) 5-block 31, [ 9, 4, 2 ]
2.Sym(15) 5-block 30, [ 8, 4, 3 ]
2.Sym(13) 5-block 21, [ 9, 4 ]
2.Sym(13) 5-block 20, [ 9, 4 ]
2.Sym(13) 5-block 19, [ 7, 4, 2 ]
2.Sym(12) 5-block 24, [ 8, 3, 1 ]
2.Sym(12) 5-block 23, [ 8, 3, 1 ]
2.Sym(11) 5-block 17, [ 8, 3 ]
2.Sym(11) 5-block 16, [ 8, 3 ]
2.Sym(10) 5-block 20, [ 7, 2, 1 ]
2.Sym(10) 5-block 19, [ 7, 2, 1 ]
2.Sym(10) 5-block 18, [ 6, 3, 1 ]
2.Sym(10) 5-block 17, [ 6, 3, 1 ]
2.Alt(9) 5-block 12, [ 7, 2 ]
2.Alt(9) 5-block 11, [ 6, 2, 1 ]
2.Alt(9) 5-block 10, [ 6, 2, 1 ]
2.Alt(7) 5-block 8, [ 6, 2 ]
2.Alt(7) 5-block 7, [ 4, 3 ]
2.Alt(6) 5-block 7, [ 4, 2 ]
2.Alt(6) 5-block 6, [ 4, 2 ]
2.Alt(18) 5-block 26, [ 11, 6, 1 ]
2.Alt(18) 5-block 24, [ 8, 6, 3, 1 ]
2.Alt(18) 5-block 23, [ 8, 6, 3, 1 ]
2.Alt(16) 5-block 24, [ 9, 4, 3 ]
2.Alt(16) 5-block 22, [ 7, 6, 2, 1 ]
2.Alt(16) 5-block 21, [ 7, 6, 2, 1 ]
2.Alt(15) 5-block 22, [ 9, 4, 2 ]
2.Alt(15) 5-block 21, [ 9, 4, 2 ]
2.Alt(15) 5-block 20, [ 8, 4, 3 ]
2.Alt(15) 5-block 19, [ 8, 4, 3 ]
2.Alt(13) 5-block 14, [ 9, 4 ]
2.Alt(13) 5-block 13, [ 7, 4, 2 ]
2.Alt(13) 5-block 12, [ 7, 4, 2 ]
2.Alt(12) 5-block 17, [ 8, 3, 1 ]
2.Alt(11) 5-block 10, [ 8, 3 ]
2.Alt(10) 5-block 11, [ 7, 2, 1 ]
2.Alt(10) 5-block 10, [ 6, 3, 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