C₃×((C₂²⋊C₉)⋊C₂)⋊C₃ #10620040

order	648
isoclinism	isoclinic class of ((C₂²⋊C₉)⋊C₂)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×((C₂²⋊C₉)⋊C₂)⋊C₃
unambiguous semidirect product	((C₂²⋊C₉)⋊C₂)⋊C₃²
unambiguous semidirect product	(C₃×(C₂²⋊C₉)⋊C₂)⋊C₃

	subgroup	G/H
center, hypercenter	C₃	((C₂²⋊C₉)⋊C₂)⋊C₃
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂×C₃²
Frattini	C₃	C₃²×S₄
Fitting	C₂²×C₃³	D₃
socle	C₂²×C₃²	C₃×D₃
LCS	G ▷ C₂²⋊C₉
UCS	C₁ ◁ C₃

136 conjugacy classes of subgroups.

μ_t(G) = 36

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 559);