Finite Group Databasebeta

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C₃×C₅×C₁₆×C₄₃ #72188952

order	10320
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄²×C₇ (order 2688) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄²×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₃₂₀
abelian	C₃×C₅×C₁₆×C₄₃
multiplicative	(ℤ/10321)ˣ, (ℤ/20642)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃×C₅×C₄₃
socle, prime radical	C₂×C₃×C₅×C₄₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10320 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₃₂₀, D₂₀₆₄₀
maximal subgroup of	C₃×C₅×C₃₂×C₄₃, C₂×C₃×C₅×C₁₆×C₄₃, C₃²×C₅×C₁₆×C₄₃, …
maximal normal subgroup of	C₃×C₅×C₃₂×C₄₃, C₂×C₃×C₅×C₁₆×C₄₃, C₃²×C₅×C₁₆×C₄₃, …
maximal quotient of	C₃×C₅×C₃₂×C₄₃, C₂×C₃×C₅×C₁₆×C₄₃, C₃²×C₅×C₁₆×C₄₃, …
automorphism group of	C₁₀₃₂₁
outer automorphism group of	C₁₀₃₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.