C₃⋊(C₉⋊((C₂²⋊C₉)⋊C₂)) #14518112

order	1944
isoclinism	isoclinic class of C₃⋊(C₉⋊((C₂²⋊C₉)⋊C₂))
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂×C₃²×C₉

Aliases

unambiguous semidirect product	C₃⋊(C₉⋊((C₂²⋊C₉)⋊C₂))
unambiguous semidirect product	C₉⋊(C₃⋊((C₂²⋊C₉)⋊C₂))

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

654 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.

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

μ_t(G) = 486

Polycyclic presentation:

2,3^5,2^2|b^3=f,d^3=e,b^a=b^2f^2,c^a=c^2,d^a=d^2e^2,e^a=e^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, 2506);