C₃⋊(#1712⋊C₃) #11920147

order	1152
isoclinism	isoclinic class of C₃⋊(#1712⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₈

Aliases

unambiguous semidirect product	C₃⋊(#1712⋊C₃)
unambiguous semidirect product	#68062⋊C₃

C₃×C₈² ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₈²	C₂×C₃
Frattini	C₄²	D₃×A₄
socle	C₂²×C₃	#127⋊C₃
LCS	G ▷ C₃×C₈²
UCS	C₁

124 conjugacy classes of subgroups.

μ_t(G) = 72

Polycyclic presentation:

2,3,2^2,3,2^4|c^2=g,d^2=fghi,f^2=h,g^2=i,c^a=cgi,d^a=dfg,e^a=e^2,f^a=fh,g^a=gi,c^b=d,d^b=cdf,f^b=g,g^b=fghi,h^b=i,i^b=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154158);