Dic₃² #3720

order	144
isoclinism	isoclinic class of D₃²
automorphism	Aut(G) = #11856169 (order 1152) · Inn(G) = D₃² · Out(G) = #120
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

C₃² ⋊ C₄²

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃²
commutator, hypocenter	C₃²	C₄²
Fitting, socle, prime radical, cosocle	C₂²×C₃²	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 48

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 63);