#10339⋊C₃ #11709147

order	768
isoclinism	isoclinic class of #10339⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#1304	C₂×C₃
Frattini	C₂⁵	C₂×A₄
Fitting	#10339	C₃
socle	C₂²	#392⋊C₃
prime radical	#1304⋊C₃	C₂
LCS	G ▷ #1304
UCS	C₁

148 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 32

Polycyclic presentation:

3,2^8|b^2=h,c^2=h,d^2=i,b^a=dghi,c^a=bgh,d^a=cefh,e^a=fhi,f^a=gh,g^a=e,h^a=i,i^a=hi,c^b=ce,d^b=df,g^b=ghi,d^c=dg,f^c=fi,e^d=eh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083528);