C₂²×C₃⋊S₄ #64386

order	288
isoclinism	isoclinic class of C₃⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

C₂²×C₃⋊S₄

Fitting, socle	C₂⁴×C₃ ⋊ D₃
derived	C₃×A₄ ⋊ C₂³

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊S₄
commutator, cosocle, hypocenter	C₃×A₄	C₂³
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃	D₃
LCS	G ▷ C₃×A₄
UCS	C₁ ◁ C₂²

326 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 3 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1034);