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C₂×C₅×C₉×C₁₈₁ #30654306

order	16290
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄²×C₅×C₉ (order 4320) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄²×C₅×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₂₉₀
abelian	C₂×C₅×C₉×C₁₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅×C₁₈₁
socle, prime radical	C₂×C₃×C₅×C₁₈₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16290 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₆₂₉₀, D₃₂₅₈₀
maximal subgroup of	C₄×C₅×C₉×C₁₈₁, C₅×C₉×Dic₁₈₁, C₉×Dic₅×C₁₈₁, …
maximal normal subgroup of	C₄×C₅×C₉×C₁₈₁, C₅×C₉×Dic₁₈₁, C₉×Dic₅×C₁₈₁, …
maximal quotient of	C₄×C₅×C₉×C₁₈₁, C₂²×C₅×C₉×C₁₈₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16290, 1);