#14518190

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

Aliases

No aliases for this group.

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

292 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

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

μ_t(G) = 54

Polycyclic presentation:

2,3^2,2^2,3^3|b^3=h^2,f^a=f^2,g^a=g^2h,c^b=ch^2,d^b=de,e^b=d,f^b=fg,g^f=gh

maximal subgroup of	#72276187, #72276237
maximal normal subgroup of	#72276237

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2584);