D₃×C₂²⋊A₄ #64390

order	288
isoclinism	isoclinic class of D₃×C₂²⋊A₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	D₃×C₂²⋊A₄
unambiguous semidirect product	C₃⋊(C₂×C₂²⋊A₄)

C₂⁴×C₃ ⋊ C₂×C₃

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

303 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1038);