Finite Group Databasebeta

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C₅×C₁₁×C₁₃×C₁₆ #72189891

order	11440
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄³×C₅ (order 3840) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄³×C₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₄₄₀
abelian	C₅×C₁₁×C₁₃×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₅×C₁₁×C₁₃
socle, prime radical	C₂×C₅×C₁₁×C₁₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11440 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₄₄₀, D₂₂₈₈₀
maximal subgroup of	C₅×C₁₁×C₁₃×C₃₂, C₂×C₅×C₁₁×C₁₃×C₁₆, D₁₁₄₄₀, …
maximal normal subgroup of	C₅×C₁₁×C₁₃×C₃₂, C₂×C₅×C₁₁×C₁₃×C₁₆, D₁₁₄₄₀, …
maximal quotient of	C₅×C₁₁×C₁₃×C₃₂, C₂×C₅×C₁₁×C₁₃×C₁₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.