D₃³⋊C₃ #10620186

order	648
isoclinism	isoclinic class of D₃³⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

D₃³⋊C₃

Fitting, socle	C₃³ ⋊ C₂×A₄
derived	#1113 ⋊ C₂×C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	#1113	C₂×C₃
Fitting, socle	C₃³	C₂×A₄
LCS	G ▷ #1113
UCS	C₁

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 9
transitive degree	μ_t(G) = 9

Polycyclic presentation:

2,3,2^2,3^3|e^a=e^2,f^a=f^2,g^a=g^2,c^b=d,d^b=cd,e^b=f,f^b=g,g^b=e,e^c=e^2,g^c=g^2,e^d=e^2,f^d=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 705);