A₄⋊#4181 #14518097

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

Aliases

Fitting	C₂²×C₃²⋊C₉ ⋊ D₃
derived	A₄×C₃²⋊C₉ ⋊ C₂

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₉⋊S₄)
commutator, cosocle, hypocenter	A₄×C₃²⋊C₉	C₂
Frattini	C₃²	C₃⋊(C₃⋊S₄)
Fitting	C₂²×C₃²⋊C₉	D₃
socle	C₂²×C₃²	C₃⋊(C₃⋊D₃)
LCS	G ▷ A₄×C₃²⋊C₉
UCS	C₁ ◁ C₃

473 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 473 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

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

μ_t(G) = 72

Polycyclic presentation:

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

maximal subgroup of	#72259969
maximal normal subgroup of	#72259969

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2491);