C₂³×C₄²⋊C₃ #85568

order	384
isoclinism	isoclinic class of C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

C₂³×C₄²⋊C₃

Fitting, Sylow	C₂³×C₄² ⋊ C₃
derived	C₄² ⋊ C₂³×C₃

	subgroup	G/H
center, hypercenter	C₂³	C₄²⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂³×C₃
Frattini	C₂²	C₂³×A₄
Fitting	C₂³×C₄²	C₃
socle	C₂⁵	A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₂³

580 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 16 points:

(5,9,11,6,7,13)(8,14,15,10,12,16);(3,4)(7,12,9,14)(11,16,13,15);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18144);