C₂²×D₃×A₄ #64389

order	288
isoclinism	isoclinic class of D₃×A₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₂²×D₃×A₄
unambiguous semidirect product	C₃⋊(C₂³×A₄)
unambiguous semidirect product	(C₂×C₃)⋊(C₂²×A₄)

Fitting, socle	C₂⁴×C₃ ⋊ C₂×C₃
derived	C₂²×C₃ ⋊ C₂³×C₃

	subgroup	G/H
center, hypercenter	C₂²	D₃×A₄
commutator, cosocle, hypocenter	C₂²×C₃	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃	C₂×C₃
LCS	G ▷ C₂²×C₃
UCS	C₁ ◁ C₂²

366 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1037);