#14518597

order	1944
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	C₃⋊(C₃⋊#157)
commutator, hypocenter	C₃²×H(3,𝔽₃)	C₈
Fitting, prime radical	C₂×C₃²×H(3,𝔽₃)	C₄
socle	C₂×C₃³	C₃⋊Dic₃
cosocle	H(3,𝔽₃)×C₃⋊Dic₃	C₂
LCS	G ▷ C₃²×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

346 conjugacy classes of subgroups.

μ_t(G) = 72

Polycyclic presentation:

2^3,3^5|a^2=b,b^2=c,d^a=de,e^a=de^2,f^a=f^2,g^a=g^2,d^b=d^2,e^b=e^2,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2991);