C₃⋊(C₃⋊(C₉⋊S₄)) #14519227

order	1944
isoclinism	isoclinic class of C₃⋊(C₃⋊(C₉⋊S₄))
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂×C₃⁶

Aliases

unambiguous semidirect product	C₃⋊(C₃⋊(C₉⋊S₄))
unambiguous semidirect product	C₉⋊(C₃⋊(C₃⋊S₄))
unambiguous semidirect product	A₄⋊(C₃⋊(C₃⋊D₉))

Fitting	C₂²×C₃²×C₉ ⋊ D₃
derived	C₃²×C₉×A₄ ⋊ C₂

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃²×C₉×A₄	C₂
Frattini	C₃	C₃⋊(C₃⋊(C₃⋊S₄))
Fitting	C₂²×C₃²×C₉	D₃
socle	C₂²×C₃³	C₃⋊D₃
LCS	G ▷ C₃²×C₉×A₄
UCS	C₁

1734 conjugacy classes of subgroups; only the 447 normal subgroups are shown.

normal subgroups only

This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.

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

μ_t(G) = 324

Polycyclic presentation:

2,3^5,2^2|e^3=f,b^a=b^2,c^a=c^2,d^a=d^2,e^a=e^2f^2,f^a=f^2,g^a=gh,g^b=h,h^b=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3621);