#6883⋊Q₈ #14516011

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center	C₂	C₂×#6883⋊C₂
commutator, prime radical, cosocle	C₂×#732	C₂²×C₃
Frattini	C₂×C₃×C₉	C₂×C₃×D₃
Fitting	C₄×#6883	C₂
socle	C₂×C₃	C₂×#4178
hypercenter	C₄	#6883⋊C₂
hypocenter	#732	C₃×Q₈
LCS	G ▷ C₂×#732 ▷ #732
UCS	C₁ ◁ C₂ ◁ C₄

93 conjugacy classes of subgroups.

μ_t(G) = 216

Polycyclic presentation:

2^2,3,2,3^4|a^2=d,b^2=d,c^3=gh^2,f^3=h^2,b^a=bd,e^a=e^2,f^a=f^2g,g^a=gh,h^a=h^2,e^c=ef,f^c=fh,f^e=fg,g^e=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 405);