#14517728

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, socle	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)
commutator, prime radical, cosocle	C₂×C₃²⋊H(3,𝔽₃)	C₂²
Fitting	C₄×C₃²⋊H(3,𝔽₃)	C₂
hypercenter	C₃²×C₄	C₃⋊(C₃⋊D₃)
hypocenter	C₃²⋊H(3,𝔽₃)	Q₈
LCS	G ▷ C₂×C₃²⋊H(3,𝔽₃) ▷ C₃²⋊H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃² ◁ C₃²×C₄

801 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 801 conjugacy classes of subgroups — too many to draw. Only its 114 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,b^a=bc,d^a=d^2,e^a=e^2,f^a=f^2,f^d=fh,f^e=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2122);