#14516149

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

Aliases

No aliases for this group.

	subgroup	G/H
center, socle	C₂×C₃	C₂×#4185
commutator, prime radical, cosocle	C₂×#6879	C₂²
Frattini	C₂×C₃×C₉	C₂×C₃⋊D₃
Fitting	C₄×#6879	C₂
hypercenter	C₃×C₄	#4185
hypocenter	#6879	Q₈
LCS	G ▷ C₂×#6879 ▷ #6879
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

135 conjugacy classes of subgroups.

μ_t(G) = 216

Polycyclic presentation:

2^3,3^5|a^2=c,b^2=c,f^3=h^2,b^a=bc,d^a=d^2,e^a=e^2,g^a=g^2h,e^d=ef,f^d=fg,g^d=gh,f^e=fg^2h,g^e=gh^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 543);