C₂×C₅×D₉×C₁₀₁ #32911412

order	18180
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₀₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₉×C₁₀₁
unambiguous semidirect product	C₉⋊(C₂²×C₅×C₁₀₁)
unambiguous semidirect product	(C₂×C₉)⋊(C₂×C₅×C₁₀₁)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₀₁	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₅×C₁₀₁
Frattini	C₃	C₂×C₅×D₃×C₁₀₁
Fitting	C₂×C₅×C₉×C₁₀₁	C₂
socle	C₂×C₃×C₅×C₁₀₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₅×C₁₀₁

60 conjugacy classes of subgroups.

μ_t(G) = 9090

6060 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 45);