C₂²×C₄²⋊C₃ #5433

order	192
isoclinism	isoclinic class of C₄²⋊C₃
automorphism	Aut(G) = D₃×#4626⋊C₂ (order 2304) · Inn(G) = C₄²⋊C₃ · Out(G) = D₃×D₄
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

C₂²×C₄²⋊C₃

Fitting, Sylow	C₂²×C₄² ⋊ C₃
derived	C₄² ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₂²	C₄²⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂²×C₃
Frattini	C₂²	C₂²×A₄
Fitting	C₂²×C₄²	C₃
socle	C₂⁴	A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₂²

108 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 992);