#10300⋊C₃ #11709141

order	768
isoclinism	isoclinic class of #10300⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₄

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#1309	C₂×C₃
Frattini	C₂×C₄²	C₂×A₄
Fitting	#10300	C₃
socle	C₂²	#392⋊C₃
LCS	G ▷ #1309
UCS	C₁

117 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 24

Polycyclic presentation:

3,2^8|e^2=h,f^2=i,g^2=hi,b^a=ceh,c^a=df,d^a=befi,e^a=g,f^a=eh,g^a=fi,h^a=hi,i^a=h,c^b=ce,d^b=df,e^b=eh,f^b=fi,d^c=dg,e^c=eh,g^c=ghi,f^d=fi,g^d=ghi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083522);