C₂⁴×C₃⋊D₃ #64396

order	288
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

C₂⁴×C₃⋊D₃

Fitting, socle	C₂⁴×C₃² ⋊ C₂
derived, Sylow	C₃² ⋊ C₂⁵

	subgroup	G/H
center, hypercenter	C₂⁴	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂⁴

2244 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 5 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1044);