#14518844

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	C₃⋊#1113
commutator, Fitting, prime radical, cosocle	C₂×C₃²×H(3,𝔽₃)	C₂²
socle	C₂×C₃³	C₂×C₃⋊D₃
hypocenter	C₃²×H(3,𝔽₃)	Q₈
LCS	G ▷ C₂×C₃²×H(3,𝔽₃) ▷ C₃²×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

657 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 657 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

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

μ_t(G) = 72

Polycyclic presentation:

2^3,3^5|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^2,g^a=g^2,d^b=d^2,e^b=e^2,f^b=f^2,e^d=eh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3238);