#14519010

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₃⁵

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂×C₃	C₂×C₃⋊(C₃⋊(C₃⋊D₃))
commutator, prime radical, cosocle	C₂×C₃²×H(3,𝔽₃)	C₂²
Fitting	C₃²×C₄×H(3,𝔽₃)	C₂
socle	C₂×C₃³	C₂×C₃⋊D₃
hypercenter	C₃×C₄	C₃⋊(C₃⋊(C₃⋊D₃))
hypocenter	C₃²×H(3,𝔽₃)	Q₈
LCS	G ▷ C₂×C₃²×H(3,𝔽₃) ▷ C₃²×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

2052 conjugacy classes of subgroups.

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,g^a=g^2,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3404);