C₃×C₂₉×C₁₀₉⋊C₃ #43249579

order	28449
automorphism	?
homology	Abelianization (H₁) = C₃²×C₂₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₂₉×C₁₀₉⋊C₃
unambiguous semidirect product	C₁₀₉⋊(C₃²×C₂₉)
unambiguous semidirect product	(C₃×C₁₀₉)⋊(C₃×C₂₉)
unambiguous semidirect product	(C₂₉×C₁₀₉)⋊C₃²
unambiguous semidirect product	(C₃×C₂₉×C₁₀₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₂₉	C₁₀₉⋊C₃
commutator, cosocle, hypocenter	C₁₀₉	C₃²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₁₀₉	C₃
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₃×C₂₉

24 conjugacy classes of subgroups.

μ_t(G) = 9483

3393 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28449, 5);