#2845⋊C₉ #11919661

order	1152
automorphism	?
homology	Abelianization (H₁) = C₉ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, hypercenter	C₂×C₃	#564⋊C₃
commutator, hypocenter	#2845	C₉
Frattini, socle, prime radical	C₂³×C₃	C₂²⋊A₄
Fitting, cosocle	C₃×#2845	C₃
LCS	G ▷ #2845
UCS	C₁ ◁ C₂×C₃

139 conjugacy classes of subgroups.

μ_t(G) = 72

Polycyclic presentation:

3^2,2^7|a^3=b,c^2=g,d^2=i,e^2=ghi,f^2=gh,c^a=fg,d^a=de,e^a=dh,f^a=cf,g^a=gh,h^a=g,i^a=hi,d^c=dgh,e^c=eh,e^d=egi,f^d=fg,f^e=fgh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153672);