C₃×C₂₁₆₁⋊C₃ #34085557

order	19449
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₂₁₆₁⋊C₃
unambiguous semidirect product	C₂₁₆₁⋊C₃²
unambiguous semidirect product	(C₃×C₂₁₆₁)⋊C₃

Fitting, socle	C₃×C₂₁₆₁ ⋊ C₃
derived, Sylow	C₂₁₆₁ ⋊ C₃²

	subgroup	G/H
center, hypercenter	C₃	C₂₁₆₁⋊C₃
commutator, cosocle, hypocenter	C₂₁₆₁	C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₂₁₆₁	C₃
LCS	G ▷ C₂₁₆₁
UCS	C₁ ◁ C₃

12 conjugacy classes of subgroups.

μ_t(G) = 6483

2169 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19449, 4);