A₄⋊#4208 #14519221

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂×C₃²

Aliases

	subgroup	G/H
center, hypercenter	C₉	C₃⋊(C₃⋊S₄)
commutator, cosocle, hypocenter	A₄×H(3,𝔽₃)	C₂×C₃
Frattini	C₃	C₃×C₃⋊(C₃⋊S₄)
Fitting	C₂²×#737	D₃
socle	C₂²×C₃	C₃×C₃⋊(C₃⋊D₃)
prime radical	A₄⋊#272	C₃
LCS	G ▷ A₄×H(3,𝔽₃)
UCS	C₁ ◁ C₉

521 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 521 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

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

μ_t(G) = 108

Polycyclic presentation:

2,3^5,2^2|b^3=f,c^a=c^2,d^a=d^2,e^a=e^2,g^a=gh,g^c=h,h^c=gh,e^d=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3615);