D₃²⋊(C₃⋊D₃) #10620202

order	648
isoclinism	isoclinic class of D₃²⋊(C₃⋊D₃)
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₃

Aliases

D₃²⋊(C₃⋊D₃)

C₃⁴ ⋊ D₄

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₃²×C₃⋊D₃	C₂²
Fitting, socle, hypocenter	C₃⁴	D₄
LCS	G ▷ C₃²×C₃⋊D₃ ▷ C₃⁴
UCS	C₁

226 conjugacy classes of subgroups.

μ_t(G) = 36

Polycyclic presentation:

2^3,3^4|b^a=bc,d^a=d^2,e^a=d^2e,f^a=f^2,g^a=g^2,d^b=d^2e^2,d^c=d^2,e^c=e^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 721);