#14519253

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

Aliases

No aliases for this group.

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

508 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 58 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,f^a=f^2,g^a=g^2,c^b=ch,d^b=de,e^b=d,g^f=gh

maximal subgroup of	#72276187, #72276229
maximal normal subgroup of	#72276229

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3647);