A₄×#4176 #14518156

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

Aliases

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

210 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.

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

μ_t(G) = 108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2550);