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C₅×C₈×C₉×C₃₁ #72189653

order	11160
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃²×C₄×C₅ (order 2880) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃²×C₄×C₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₁₆₀
abelian	C₅×C₈×C₉×C₃₁
multiplicative	(ℤ/11161)ˣ, (ℤ/22322)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂×C₃×C₅×C₃₁
socle, prime radical	C₂×C₃×C₅×C₃₁	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11160 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₁₆₀, D₂₂₃₂₀
maximal subgroup of	C₅×C₉×C₁₆×C₃₁, C₂×C₅×C₈×C₉×C₃₁, D₁₁₁₆₀, …
maximal normal subgroup of	C₅×C₉×C₁₆×C₃₁, C₂×C₅×C₈×C₉×C₃₁, D₁₁₁₆₀, …
maximal quotient of	C₅×C₉×C₁₆×C₃₁, C₂×C₅×C₈×C₉×C₃₁
automorphism group of	C₁₁₁₆₁
outer automorphism group of	C₁₁₁₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.