Semidihedral group

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Definition

Let n be a natural number greater than or equal to 4. The semidihedral group or quasidihedral group of order 2^n (and degree 2^{n-1}), denoted SD_{2^n}, is defined by the following presentation:

\! SD_{2^n} = QD_{2^n} := \langle a,x \mid a^{2^{n-1}} = x^2 = e, xax = a ^{2^{n-2} - 1} \rangle

(here, e is the symbol for the identity element).

Particular cases

n 2^n n - 1 2^{n-1} Group
4 16 3 8 semidihedral group:SD16
5 32 4 16 semidihedral group:SD32
6 64 5 32 semidihedral group:SD64
7 128 6 64 semidihedral group:SD128