Finite Group Databasebeta

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C₃×C₁₁×C₁₆×C₁₉ #72188698

order	10032
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₄×C₅×C₉ (order 2880) · Inn(G) = C₁ · Out(G) = C₂⁴×C₄×C₅×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₀₃₂
abelian	C₃×C₁₁×C₁₆×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃×C₁₁×C₁₉
socle, prime radical	C₂×C₃×C₁₁×C₁₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10032 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₀₃₂, D₂₀₀₆₄
maximal subgroup of	C₃×C₁₁×C₁₉×C₃₂, C₂×C₃×C₁₁×C₁₆×C₁₉, C₉×C₁₁×C₁₆×C₁₉, …
maximal normal subgroup of	C₃×C₁₁×C₁₉×C₃₂, C₂×C₃×C₁₁×C₁₆×C₁₉, C₉×C₁₁×C₁₆×C₁₉, …
maximal quotient of	C₃×C₁₁×C₁₉×C₃₂, C₂×C₃×C₁₁×C₁₆×C₁₉, C₉×C₁₁×C₁₆×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.