Finite Group Databasebeta

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C₅×C₁₆×C₈₃ #72185757

order	6640
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄²×C₄₁ (order 2624) · Inn(G) = C₁ · Out(G) = C₂²×C₄²×C₄₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₆₆₄₀
abelian	C₅×C₁₆×C₈₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₅×C₈₃
socle, prime radical	C₂×C₅×C₈₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6640 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₃₂₈₀, Dic₆₆₄₀
maximal subgroup of	C₅×C₃₂×C₈₃, C₂×C₅×C₁₆×C₈₃, C₃×C₅×C₁₆×C₈₃, …
maximal normal subgroup of	C₅×C₃₂×C₈₃, C₂×C₅×C₁₆×C₈₃, C₃×C₅×C₁₆×C₈₃, …
maximal quotient of	C₅×C₃₂×C₈₃, C₂×C₅×C₁₆×C₈₃, C₃×C₅×C₁₆×C₈₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.