Linear representation theory of groups of order 96

Grouping by degrees of irreducible representations
There are 29 possibilities for the degrees of irreducible representations for the 231 groups of order 96.

Here is the GAP code to generate this:

We use the GAP function (not in-built, but coded) IrrepDegreeGroupingFull and ModifiedNilpClass (the latter simply returns the nilpotency class if the group is nilpotent and 0 otherwise):

gap> I := IrrepDegreeGroupingFull(96);; gap> List(I,x -> [x[1],Length(x[2]),Set(List(x[2],i -> ModifiedNilpClass(SmallGroup(96,i)))),Set(List(x[2],i -> DerivedLength(SmallGroup(96,i)))),x[2]]); [ [ [ [ 1, 2 ], [ 2, 1 ], [ 3, 6 ], [ 6, 1 ] ], 2, [ 0 ], [ 3 ], [ 64, 227 ] ], [ [ [ 1, 3 ], [ 2, 3 ], [ 3, 5 ], [ 6, 1 ] ], 2, [ 0 ], [ 3 ], [ 3, 203 ]    ], [ [ [ 1, 3 ], [ 3, 5 ], [ 4, 3 ] ], 1, [ 0 ], [ 3 ], [ 204 ] ], [ [ [ 1, 4 ], [ 2, 2 ], [ 3, 4 ], [ 4, 3 ] ], 3, [ 0 ], [ 4 ], [ 190, 191, 193 ] ]   , [ [ [ 1, 4 ], [ 2, 5 ], [ 3, 4 ], [ 6, 1 ] ], 3, [ 0 ], [ 3 ], [ 185, 187, 195 ] ],  [ [ [ 1, 4 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ] ], 5, [ 0 ], [ 4 ], [ 66, 67, 188, 189, 192 ] ],  [ [ [ 1, 4 ], [ 2, 11 ], [ 4, 3 ] ], 4, [ 0 ], [ 2 ], [ 33, 34, 35, 36 ] ], [ [ [ 1, 4 ], [ 2, 23 ] ], 3, [ 0 ], [ 2 ], [ 6, 7, 8 ] ],  [ [ [ 1, 6 ], [ 3, 2 ], [ 6, 2 ] ], 3, [ 0 ], [ 2 ], [ 70, 71, 72 ] ], [ [ [ 1, 6 ], [ 3, 10 ] ], 2, [ 0 ], [ 2 ], [ 68, 229 ] ],  [ [ [ 1, 8 ], [ 2, 4 ], [ 3, 8 ] ], 4, [ 0 ], [ 3 ], [ 65, 186, 194, 226 ] ],  [ [ [ 1, 8 ], [ 2, 6 ], [ 4, 4 ] ], 4, [ 0 ], [ 2 ], [ 118, 121, 122, 125 ] ],  [ [ [ 1, 8 ], [ 2, 10 ], [ 4, 3 ] ], 18, [ 0 ], [ 2 ], [ 13, 30, 31, 40, 41, 43, 115, 116, 117, 119, 120, 123, 124, 126, 139, 149, 156, 158 ] ],  [ [ [ 1, 8 ], [ 2, 14 ], [ 4, 2 ] ], 38, [ 0 ], [ 2 ], [ 14, 15, 16, 17, 29, 32, 39, 42, 44, 85, 86, 89, 90, 91, 92, 93, 95, 96, 97, 101, 102, 103,          104, 105, 138, 140, 142, 143, 144, 145, 146, 147, 148, 150, 151, 153, 154, 157 ] ],  [ [ [ 1, 8 ], [ 2, 22 ] ], 19, [ 0 ], [ 2 ], [ 12, 23, 24, 25, 26, 28, 76, 77, 81, 82, 83, 109, 110, 111, 112, 131, 136, 137, 160 ] ],  [ [ [ 1, 12 ], [ 2, 3 ], [ 3, 4 ], [ 6, 1 ] ], 2, [ 0 ], [ 2 ], [ 197, 199 ] ],  [ [ [ 1, 12 ], [ 2, 12 ], [ 3, 4 ] ], 4, [ 0 ], [ 3 ], [ 69, 74, 198, 200 ] ], [ [ [ 1, 12 ], [ 2, 21 ] ], 3, [ 4 ], [ 2 ], [ 61, 62, 63 ] ],  [ [ [ 1, 12 ], [ 3, 4 ], [ 4, 3 ] ], 2, [ 0 ], [ 3 ], [ 201, 202 ] ], [ [ [ 1, 16 ], [ 2, 8 ], [ 4, 3 ] ], 4, [ 0 ], [ 2 ], [ 211, 214, 216, 217 ] ],  [ [ [ 1, 16 ], [ 2, 12 ], [ 4, 2 ] ], 17, [ 0 ], [ 2 ], [ 84, 87, 88, 94, 98, 99, 100, 113, 114, 141, 152, 155, 209, 210, 212, 213, 215 ] ],  [ [ [ 1, 16 ], [ 2, 20 ] ], 25, [ 0 ], [ 2 ], [ 5, 10, 11, 19, 21, 22, 27, 37, 38, 75, 79, 80, 107, 108, 128, 130, 132, 133, 134, 135, 159, 205, 207,          208, 219 ] ], [ [ [ 1, 24 ], [ 2, 6 ], [ 4, 3 ] ], 5, [ 3 ], [ 2 ], [ 49, 50, 51, 183, 184 ] ],  [ [ [ 1, 24 ], [ 2, 18 ] ], 19, [ 2, 3 ], [ 2 ], [ 52, 53, 54, 56, 57, 58, 167, 168, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182 ] ],  [ [ [ 1, 24 ], [ 3, 8 ] ], 3, [ 0 ], [ 2 ], [ 73, 196, 228 ] ],  [ [ [ 1, 32 ], [ 2, 16 ] ], 12, [ 0 ], [ 2 ], [ 1, 4, 9, 18, 20, 78, 106, 127, 129, 206, 218, 230 ] ],  [ [ [ 1, 48 ], [ 2, 12 ] ], 15, [ 2 ], [ 2 ], [ 45, 47, 48, 55, 60, 162, 163, 164, 165, 166, 177, 178, 221, 222, 223 ] ],  [ [ [ 1, 48 ], [ 4, 3 ] ], 2, [ 2 ], [ 2 ], [ 224, 225 ] ], [ [ [ 1, 96 ] ], 7, [ 1 ], [ 1 ], [ 2, 46, 59, 161, 176, 220, 231 ] ] ]