Finite Group Databasebeta

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C₂×C₅×C₁₃×C₈₁ #72189137

order	10530
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄²×C₂₇ (order 2592) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄²×C₂₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₅₃₀
abelian	C₂×C₅×C₁₃×C₈₁
multiplicative	(ℤ/10531)ˣ, (ℤ/21062)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₂×C₃×C₅×C₁₃
socle, prime radical	C₂×C₃×C₅×C₁₃	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10530 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₅₃₀, D₂₁₀₆₀
maximal subgroup of	C₄×C₅×C₁₃×C₈₁, C₂²×C₅×C₁₃×C₈₁, C₂×C₅×C₁₃×C₂₄₃, …
maximal normal subgroup of	C₄×C₅×C₁₃×C₈₁, C₂²×C₅×C₁₃×C₈₁, C₂×C₅×C₁₃×C₂₄₃, …
maximal quotient of	C₄×C₅×C₁₃×C₈₁, C₂²×C₅×C₁₃×C₈₁, C₂×C₅×C₁₃×C₂₄₃, …
automorphism group of	C₁₀₅₃₁
outer automorphism group of	C₁₀₅₃₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.