A₄⋊#4176 #14518030

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

Aliases

	subgroup	G/H
center, hypercenter	C₃	A₄⋊((C₃⋊D₃)⋊C₃)
commutator, cosocle, hypocenter	A₄×H(3,𝔽₃)	C₂×C₃
Frattini	C₃²	C₃×C₃⋊S₄
Fitting	C₂²×#731	D₃
socle	C₂²×C₃	C₃⋊((C₃⋊D₃)⋊C₃)
prime radical	A₄⋊#272	C₃
LCS	G ▷ A₄×H(3,𝔽₃)
UCS	C₁ ◁ C₃

212 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 26 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^2,c^a=c^2,d^a=d^2,e^a=e^2f,g^a=gh,d^b=de,g^c=h,h^c=gh,e^d=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2424);