#14517740

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₃³

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂	C₂×C₃⋊#4185
commutator, prime radical, cosocle	C₂×C₃×#732	C₂²
Frattini	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)
Fitting	C₃×C₄×#732	C₂
socle	C₂×C₃²	C₂×#272
hypercenter	C₄	C₃⋊#4185
hypocenter	C₃×#732	Q₈
LCS	G ▷ C₂×C₃×#732 ▷ C₃×#732
UCS	C₁ ◁ C₂ ◁ C₄

450 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

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

μ_t(G) = 648

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2134);