Linear representation theory of semidihedral groups

This article gives specific information, namely, linear representation theory, about a family of groups, namely: semidihedral group.
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Summary

The summary below is for a semidihedral group of order $2^{n}$. The order of the cyclic maximal subgroup is $2^{n-1}$, and the nilpotency class is $n-1$.

Item	Value
degrees of irreducible representations over a splitting field	degree 1 (4 times) and degree 2 ($2^{n-2}-1$ times)
number of irreducible representations	$2^{n-2}+3$ See number of irreducible representations equals number of conjugacy classes, element structure of semidihedral groups
maximum degree of irreducible representation over a splitting field	2 See also degree of irreducible representation divides index of abelian normal subgroup
sum of squares of degrees of irreducible representations over a splitting field	$2^{n}$, equal to the group order. See sum of squares of degrees of irreducible representations equals order of group

Particular cases

Value $n$	$2^{n}$	$2^{n-1}$	Semidihedral group of order $2^{n}$	Number of irreps of degree 1 (= 4)	Number of irreps of degree 2 (= $2^{n-2}-1$)	Total number of irreps (= $2^{n-2}+3$)	Linear representation theory page
4	16	8	semidihedral group:SD16	4	3	7	linear representation theory of semidihedral group:SD16
5	32	16	semidihedral group:SD32	4	7	11	linear representation theory of semidihedral group:SD32
6	64	32	semidihedral group:SD64	4	15	19	linear representation theory of semidihedral group:SD64
7	128	64	semidihedral group:SD128	4	31	35	linear representation theory of semidihedral group:SD128