C₂⁴×C₃×D₃ #64395

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

Aliases

direct product	C₂⁴×C₃×D₃
unambiguous semidirect product	C₃⋊(C₂⁵×C₃)
unambiguous semidirect product	(C₂×C₃)⋊(C₂⁴×C₃)

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

1563 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 96

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1043);