D₂₀₄ #87990

order	408
isoclinism	isoclinic class of Dic₁₀₂
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₂₀₄
unambiguous semidirect product	C₄⋊D₅₁

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 204

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24);(2,4)(6,7)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)

Polycyclic presentation:

2^3,3,17|b^2=c,b^a=bc,d^a=d^2,e^a=e^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 27);