#14517746

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₃²

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂	C₂×#92344
commutator, prime radical, cosocle	C₂×#6908	C₂²
Frattini	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)
Fitting	C₄×#6908	C₂
socle	C₂×C₃	C₂×C₃⋊#272
hypercenter	C₄	#92344
hypocenter	#6908	Q₈
LCS	G ▷ C₂×#6908 ▷ #6908
UCS	C₁ ◁ C₂ ◁ C₄

357 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 357 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

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

μ_t(G) = 216

Polycyclic presentation:

2^3,3^5|a^2=c,b^2=c,d^3=h^2,b^a=bc,d^a=d^2h,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, 2140);