C₂²⋊(#564⋊C₃) #11710656

order	768
isoclinism	isoclinic class of C₂²⋊(#564⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₂⁹

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂²×#564	C₃
Frattini	C₂²	C₂²⋊(C₂²⋊A₄)
socle	C₂⁴	C₂²⋊A₄
LCS	G ▷ C₂²×#564
UCS	C₁

1144 conjugacy classes of subgroups.

μ_t(G) = 96

Polycyclic presentation:

3,2^8|b^2=hi,c^2=h,d^2=hi,e^2=h,b^a=bceh,c^a=bdefgh,d^a=ef,e^a=defghi,f^a=gh,g^a=fghi,h^a=i,i^a=hi,c^b=ch,d^b=di,e^b=eh,d^c=dhi,e^c=ei

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1085037);