Finite Group Databasebeta

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C₅×C₁₆×C₁₂₁ #72188384

order	9680
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄²×C₅×C₁₁ (order 3520) · Inn(G) = C₁ · Out(G) = C₂²×C₄²×C₅×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₆₈₀
abelian	C₅×C₁₆×C₁₂₁

Subgroups

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

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9680 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₆₈₀, D₁₉₃₆₀
maximal subgroup of	C₅×C₃₂×C₁₂₁, C₂×C₅×C₁₆×C₁₂₁, C₃×C₅×C₁₆×C₁₂₁, …
maximal normal subgroup of	C₅×C₃₂×C₁₂₁, C₂×C₅×C₁₆×C₁₂₁, C₃×C₅×C₁₆×C₁₂₁, …
maximal quotient of	C₅×C₃₂×C₁₂₁, C₂×C₅×C₁₆×C₁₂₁, C₃×C₅×C₁₆×C₁₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.