#2810⋊C₉ #11919649

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

Aliases

	subgroup	G/H
center, hypercenter	C₂×C₃	#564⋊C₃
commutator, hypocenter	#2810	C₉
Frattini, socle, prime radical	C₂³×C₃	C₂²⋊A₄
Fitting, cosocle	C₃×#2810	C₃
LCS	G ▷ #2810
UCS	C₁ ◁ C₂×C₃

145 conjugacy classes of subgroups.

μ_t(G) = 72

Polycyclic presentation:

3^2,2^7|a^3=b,c^2=h,d^2=g,e^2=h,f^2=g,c^a=dh,d^a=cd,e^a=fh,f^a=ef,g^a=gh,h^a=g,i^a=hi,e^c=ehi,f^c=fg,e^d=ei,f^d=fghi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153660);