Linear representation theory of groups of order 96

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This article gives specific information, namely, linear representation theory, about a family of groups, namely: groups of order 96.
View linear representation theory of group families | View linear representation theory of groups of a particular order |View other specific information about groups of order 96

Degrees of irreducible representations

FACTS TO CHECK AGAINST FOR DEGREES OF IRREDUCIBLE REPRESENTATIONS OVER SPLITTING FIELD:
Divisibility facts: degree of irreducible representation divides group order | degree of irreducible representation divides index of abelian normal subgroup
Size bounds: order of inner automorphism group bounds square of degree of irreducible representation| degree of irreducible representation is bounded by index of abelian subgroup| maximum degree of irreducible representation of group is less than or equal to product of maximum degree of irreducible representation of subgroup and index of subgroup
Cumulative facts: sum of squares of degrees of irreducible representations equals order of group | number of irreducible representations equals number of conjugacy classes | number of one-dimensional representations equals order of abelianization

Grouping by degrees of irreducible representations

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

Number of irreps of degree 1 Number of irreps of degree 2 Number of irreps of degree 3 Number of irreps of degree 4 Number of irreps of degree 6 Total number of irreducible representations = number of conjugacy classes Number of groups with these irreps Nilpotency class(es) attained Derived lengths attained Description of groups List of GAP IDs (second part)
96 0 0 0 0 96 7 1 1 the abelian groups 2, 46, 59, 161, 176, 220, 231
48 12 0 0 0 60 15 2 2  ? [SHOW MORE]
48 0 0 3 0 51 2 2 2  ? 224, 225
32 16 0 0 0 48 12 not nilpotent 2  ? [SHOW MORE]
24 18 0 0 0 42 19 2, 3 2  ? [SHOW MORE]
24 6 0 3 0 33 5 3 2  ? 49, 50, 51, 183, 184
24 0 8 0 0 32 3 not nilpotent 2  ? 73, 196, 228
16 20 0 0 0 36 25 not nilpotent 2  ? [SHOW MORE]
16 12 0 2 0 30 17 not nilpotent 2  ? [SHOW MORE]
16 8 0 3 0 27 4 not nilpotent 2  ? 211, 214, 216, 217
12 21 0 0 0 33 3 4 2  ? 61, 62, 63
12 12 4 0 0 28 4 not nilpotent 3  ? 69, 74, 198, 200
12 3 4 0 1 20 2 not nilpotent 2  ? 197, 199
12 0 4 3 0 19 2 not nilpotent 3  ? 201, 202
8 22 0 0 0 30 19 not nilpotent 2  ? [SHOW MORE]
8 14 0 2 0 24 38 not nilpotent 2  ? [SHOW MORE]
8 10 0 3 0 21 18 not nilpotent 2  ? [SHOW MORE]
8 6 0 4 0 18 4 not nilpotent 2  ? 118, 121, 122, 125
8 4 8 0 0 20 4 not nilpotent 3  ? 65, 186, 194, 226
6 0 10 0 0 16 2 not nilpotent 2  ? 68, 229
6 0 2 0 2 10 3 not nilpotent 2  ? 70, 71, 72
4 23 0 0 0 27 3 not nilpotent 2  ? 6, 7, 8
4 11 0 3 0 18 4 not nilpotent 2  ? 33, 34, 35, 36
4 6 4 2 0 16 5 not nilpotent 4  ? 66, 67, 188, 189, 192
4 5 4 0 1 14 3 not nilpotent 3  ? 185, 187, 195
4 2 4 3 0 13 3 not nilpotent 4  ? 190, 191, 193
3 3 5 0 1 12 2 not nilpotent 3  ? 3, 203
3 0 5 3 0 11 1 not nilpotent 3  ? 204
2 1 6 0 1 10 2 not nilpotent 3  ? 64, 227
Here is the GAP code to generate this:[SHOW MORE]