C₂×A₄×C₁₆ #73273

order	384
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×A₄×C₁₆
unambiguous semidirect product	(C₂³×C₁₆)⋊C₃

Fitting, Sylow	C₂³×C₁₆ ⋊ C₃
derived	C₂² ⋊ C₂×C₃×C₁₆

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5849);