Linear representation theory of groups of order 72

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This article gives specific information, namely, linear representation theory, about a family of groups, namely: groups of order 72.
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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

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 Number of irreps of degree 8 Total number of irreps = number of conjugacy classes Number of groups with these degrees of irreps Nilpotency class(es) attained Derived lengths attained Description of groups List of GAP IDs (second part)
72 0 0 0 0 0 72 6 1 1 abelian groups 2, 9, 14, 18, 36, 50
36 9 0 0 0 0 45 4 2 2  ? 10, 11, 37, 38
24 12 0 0 0 0 36 4 not nilpotent 2  ? 12, 27, 29, 48
18 0 6 0 0 0 24 2 not nilpotent 2  ? 16, 47
12 15 0 0 0 0 27 3 not nilpotent 2  ? 26, 28, 30
9 9 3 0 0 0 21 2 not nilpotent 3  ? 3, 25
8 0 0 0 0 1 9 1 not nilpotent 2  ? 39
8 0 0 4 0 0 12 2 not nilpotent 2  ? 19, 45
8 16 0 0 0 0 24 8 not nilpotent 2  ? 1, 5, 7, 13, 17, 32, 34, 49
8 8 0 2 0 0 18 3 not nilpotent 2  ? 20, 21, 46
6 3 6 0 0 0 15 1 not nilpotent 3  ? 42
6 3 2 0 1 0 12 1 not nilpotent 2  ? 44
4 17 0 0 0 0 21 6 not nilpotent 2  ? 4, 6, 8, 31, 33, 35
4 9 0 2 0 0 15 3 not nilpotent 2  ? 22, 23, 24
4 1 0 0 0 1 6 1 not nilpotent 3  ? 41
4 1 0 4 0 0 9 1 not nilpotent 3  ? 40
2 4 2 0 1 0 9 2 not nilpotent 3  ? 15, 43