C₃⋊#10619772 #14518256

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

Aliases

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

369 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 33 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:

2,3,2^2,3^4|b^3=h,e^a=e^2,f^a=f^2,g^a=g^2,c^b=d,d^b=cd,f^b=fgh,g^f=gh^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2650);